I have been told that if I slow down today from 24 hours to 30, I'd end up getting hotter days, colder nights and more intense weather. That's fine, except that Earth's diverse climate makes that statement broad. So what would the SPECIFIC consequences be?
The changes will depend where you stand. If your close to the oceans, the changes will be minimized. The reason is that water takes more time to absorb the heat and takes more time to dissipate it. Also, oceans currents are better to distribute the energy than the winds overland. Overall, It would not be hotter : the days are longer but so does the nights. it just give more time to build up the heat but over the oceans the process is slower than overland.
Over the land, the change will increase the diurnal temperature range. Days will be hotter but night will be colder too. This problem would be exacerbated (like in the real world) by a low humidity. Meaning the deserts would have the biggest temperature range. Oceanic climates like Western Europe on the other hand, would be less affected since the dominant winds are pushing the humidity form the Atlantic ocean inland.
Thus all this would make the interior of the continents less pleasant places to live: increase in heat waves and freezing temperatures. It also means more extreme weather conditions as the difference in temperature between the oceans and the land increases. When the land is hot it will pull the air from the ocean further inland. When it's cold, the winds will blow toward the sea, like the Siberian highs. This could make winter drier and colder but summers wetter and could lessen the heating if there is a sufficient cloud cover and enough precipitations from the sea to cool off the land.
The major temperature swing overland could make weather systems like the Jet steam, subtropical stream, more unstable and erratic (less predictable). They change following the difference of temperature (this influences the air pressure that drives them). Generally, higher temperature range means more winds and stronger Jets. As North America and Asia would heat up faster than the oceans surrounding them, it will increase the pressure difference and thus increase the strength of the (polar) Jet stream.
This is my answer. It's probably incomplete but as the other mentioned, it would require some serious climate model to answer the question with more details.
The extended solar heating duration at the equatorial region may drive that edge of the Hadley Cell to higher altitudes. This would probably move the northern edge of this cell farther north, moving the 'desert formation' region with it. The ITCZ (The Inter Tropical Convergence Zone) would vary farther North over landmasses as well, causing the tropical rainforest and wet/dry or savanna regions to expand as well.
The storm belts should see more activity as well, with longer heating times driving formation of higher and hence larger/stronger hurricanes. The midwest's tornado alley may slide farther north as well, causing tornadoes to become more common in the northern U.S.
The longer days of course come with longer nights, so inland areas, due to continentalty, will see more extreme variation in temperatures.
I'm not sure about the mechanics on the formation of the Polar cell, but intuitively if the extra daytime drives the Hadley cell North, the extra darkness should drive the Polar cell south? This might effectively 'tighten' the temperate climate zone farther then it already is.
All guesswork of course, since even our climatologists with supercomputer driven models seem to be struggling over the effects of changing the temperature a few degrees.
If you just slow down the planet like Earth, then yes. More action of the Sun will increase the overall planet temperature. There will be more water with less ice on the poles. More water heated by the sun results in more clouds and more rain and very little clear sky above you. The atmosphere will be very hot because of the greenhouse effect. In the end, we will get something akin to Venus, but much colder. There will no Sun in the sky, because clouds will cover it all; there will be a hot and wet climate. But you can avoid all this trouble by moving the planet a little far away from the star, and, maybe, expand it diameter a little. Then you can get an Earth-like climate with a 30 hours day cycle.