The beginning of 22nd century. Temperatures on the globe rose by 30 degrees Celsius over decades, because humanity was unwilling to stop greenhouse gas emissions. How would the surface of Earth look by that time?
It is very unlikely that the Earth would warm by that degree in such a short period of time. However if it did then many parts of the planet would be uninhabitable outside of specially constructed habitats. Any areas which today have temperatures normally reaching 20 degrees C or more for an extended period would become uninhabitable without such habitats.
The sea level would dramatically rise by many metres so many coastal cities like New York, Boston and London would be flooded.
The temperature differences created would encourage huge storm systems that would devastate large areas.
The majority of species on Earth would go extinct as their habitats become too hot to sustain life and 99%+ of humanity would also die of starvation as food crops such as wheat and rice died. Heat exhaustion, disease and war would also claim millions of lives. Civilization as we know it would come to an end.
Many might survive in the far north and far south but finding food would be very difficult as it would be no easy matter to find suitable land for crops after the ice had retreated. Many areas would be barren rock, swamp or covered in masses of dead trees and there would not be enough resources to establish large enough agricultural areas quickly enough.
This is a map of the average temperatures year round. Everything above 40 is already highly dangerous (something that happens to Red/Orange countries a lot during the summer). Having that the whole year around will be devastating to the flora/water supply making it even harder on the people. So Red/Orange they are just uninhabitable areas.
Then we got the lightest shade of blue, again this is averages so a 30 degree increase would make summers impossible to survive without specialized equipment or measures.
Medium shade of blue would vary much on the location itself but most spots wil be hard living during the summer.
Darkest blue would have some livable areas but don't forget Canada and Russia are huge and it's average by country so the actual living space will be a slot smaller.
The landscape itself would be changed drastically, Coastal cities and areas will be flooded by the melting of the polar caps. Areas without a steady water supply (like the Nile River) will wither and burn much like is the case in Australia now. Eventually smaller rivers will dry out spreading the desert even further.
High mountainous areas will have the benefit of staying relatively cold but would also risk become desolate because the plants there won't have enough time to adapt to such a shift in climate (Humans could introduce flora that is better suited to take on the heat).
So eventually you are left with a world that is mostly a burned out desert with large chunks (Not water world level tho) below the waters. With mountain oases here and there across the northern hemisphere.
Temperatures on the globe rose by 30 degrees Celsius ... How would the surface of Earth look by that time?
It would look like Venus, because a 30 degree rise in average global temperature will trigger a water vapor driven runaway greenhouse effect.
Such a rise in temperature will cause all polar ice, glaciers, and permasnow to melt, and sea levels will also rise due to thermal expansion of the water (though this is likely to be a slow, ongoing process). Sea levels are hence likely to be as much as 250 meters higher than today, similar to during the late Cretaceous, but could be even higher - the historical maximum ca. 450 milllion years ago might have been 400 m above the current level. In the Cretaceous, ocean temperatures were 17C higher than today, and thermal expansion with +30C will be greater, but may take centuries or even millennia to take full effect. With sea levels 200 m above current level, everything that is green in the map below will be under water. With 400 m, so will everything yellow. In either case, this is where 95-99% of the world's population is living today.
On the positive side, Greenland and Antarctica will rise significantly when relieved of the weight of their ice caps, and with +30 degrees, these areas will be temperate. People will live here and on mountains in North America, Chile, North Asia, Australia, and possibly the southernmost Africa. Higher altitudes will mean cooler and more survivable climates. With less land area, the oceans will replace farmland as the most important food source. Seafood and seaweed will form the basis for most meals, supplemented by meat and milk from hardy mountain animals.
Evaporation from the seas will be far higher than today, leading to more clouds and more rain. More clouds will cool the surface, since more sunlight is reflected back into space - otherwise, temperatures would have risen even higher than the +30 degrees. Superhurricanes will be far more common, making living near the new coastlines very dangerous and requiring sturdier infrastructure everywhere. This will also make seasteading nearly impossible - floating structures are too vulnerable to hurricanes.
It's pretty much impossible to get that hot, certainly on that timescale, and probably on any timescale.
What a lot of people do not understand, is that we evolved during an ice age and are living in an interglacial period. The planet's climate is unstable with respect to perturbation in either direction.
There is a very real danger that we will trigger run-away global warming that will end the ice age. The mechanism would be a rise in temperature in Arctic regions covered with permafrost, causing permafrost to melt. This releases methane trapped by the permafrost. Methane is a potent greenhouse gas and then decomposes into CO2. This increases global warming, which increases permafrost melting, which increases global warming. It has happened several times in recent geological history, with no artificial help at all.
It's positive feedback. Once triggered it would probably be unstoppable. The end-point would probably take several thousand years to reach, because as far as we know Antarctica can't melt faster than that. After that time we would have a planet with no sea-level ice anywhere, and a stable, hot climate.
Stable, because any increase in greenhouse gases would cause evaporation of more water, which would create greater global cloud cover, which would reflect sunlight. This is stabilisation by negative feedback. This is also the state of the planet during most of the evolutionary history of complex life, so we know quite a bit about it.
It's a really bad place for large mammals which evolved as chase predators with a high metabolic rate during an ice age. (That's us humans). The tropics would be too hot and humid for human beings to survive. We die of heatstroke above certain levels of temperature and humidity. We would be restricted to the poles (and I'm not sure even there would be safe ... they would get pretty hot and humid during the several months of continuous sunlight and it would take only one plume of extreme heat and humidity to be fatal to us).
It's a great place for giant reptiles.
I fear that we'll carry on ignoring global warming, until a city somewhere is killed by an extreme heat/humidity excursion, and a power failure so that air-conditioning cannot save people. A million or more people suddenly dead will convince all the global warming deniers to shut up, and start trying to cover their tracks before they join the CEOs of fossil fuel companies who will face the mobs and end up dangled from lamp posts by their necks (or worse).
A great cry will go up that something must be done, but it's probably far too late at this time. But this is Worldbuilding, so you can imagine geo-engineering solutions, which might succeed in arresting the runaway warming ... and might then throw us back into a glaciation event. Unstable, remember?
More importantly the question is, I would argue, not what the earth looks like, but what is left of civilization on this disrupted earth!
It is not an incremental water level rise or the increasing temperature that is likely to be the immediate threat in some of our futures. I suggest one studies what happen to the essence of civilized man in communities hit hard by Hurricane Katrina in Lousiana in the aftermath of the storm.
Even though many knew for sure that things would get back to normal, in a matter of weeks, as people became short on food and drinking water, people started to individually rob their neighbors, or in combination via gangs for survival. That scares me more than a new high temperature on my porch's thermometer.
Actually, having experienced an air conditioning outage for a week, I also discovered, first hand, what it is like to suffer from heat exhaustion. Many of us may indeed fall victim to it before any unwelcome neighbors arrive.
Once, I also tried a juice fast for a week, with all the juice I could drink with also vitamin and mineral supplements. In under five days, I felt like a walking zombie.
So locally, one might expect as (or when) food chains become disrupted by increasingly more powerful storms from, say, over-heated oceans 'civilization' itself may also start to melt, and short on air-conditioning and food, you may not be yourself either.
Such a rise of temperature in such a short time is believed to be impossible. But let's suppose it happens anyway.
A 2013 study suggests that each 1ºC degree increase in the average temperature of the planet would cause a sea level rise of about 2.3m. I think this relationship should only be so linear for the very first few degrees, but let's do roundings and assume this is true.
30ºC would then mean the sea level would be 69 meters higher. This does not bode well for many coastal cities. The graph below is the closes approximation I could find. It is for a 80m rise, which is about 12% more than my prediction, but it does give the impression I'm aiming for.
Take a really careful look at the map at the top right corner. Southeast Asia, most of Africa and most of the Middle East remain, but everywhere else loses more than half their total land surface.
Whatever remains above the sea level will be expletively hot for today's standards of whomever lives there. See A.bakker's awesome answer on that. Also consider what Slarty had to say about crops. The areas that are still unflooded might become deserts, and food will be very hard to grow anywhere.
The picture I have in my mind is the Fallout series of games, without the mutants, but with constant inclement weather.