Even hundreds of millions of years in the future the Earth might still be in the Quaternary Ice Age which only started 2.6 million years ago. Currently we are in an intergalacial period. Anthropogenic warming will delay the onset of the next glacial phase for, possibly, another one hundred thousand years. Most likely this will only be a brief hiatus for the Quaternary Ice Age.
It is useful to look at the history of the Ice Ages to understand what might happen hundreds of millions of years in the future with respect to glaciation.
The Earth is passing through an ice age known as the quaternary glaciation, and is presently in the Holocene interglacial period. This period would normally be expected to end in about 25,000 years.[34] However, the increased rate of carbon dioxide release into the atmosphere by humans may delay the onset of the next glacial period until at least 50,000–130,000 years from now. On the other hand, a global warming period of finite duration (based on the assumption that fossil fuel use will cease by the year 2200) will probably only impact the glacial period for about 5,000 years. Thus, a brief period of global warming induced through a few centuries worth of greenhouse gas emission would only have a limited impact in the long term.
Please note this source differs in its estimate of the impact of global warming from this answer. That estimate was based on Curt Stager's book Deep Future: The Next 100,00 Years of Life Earth (2011). Who said predicting the future was easy?
A considerable number of factors affecting the future of the Earth can be discovered here. This to summarize concisely, but here are some of the salient factors.
Human Influence
Humans play a key role in the biosphere, with the large human population dominating many of Earth's ecosystems.3 This has resulted in a widespread, ongoing mass extinction of other species during the present geological epoch, now known as the Holocene extinction. The large-scale loss of species caused by human influence since the 1950s has been called a biotic crisis, with an estimated 10% of the total species lost as of 2007.[6] At current rates, about 30% of species are at risk of extinction in the next hundred years.[15] The Holocene extinction event is the result of habitat destruction, the widespread distribution of invasive species, hunting, and climate change.[16][17] In the present day, human activity has had a significant impact on the surface of the planet. More than a third of the land surface has been modified by human actions, and humans use about 20% of global primary production.[4] The concentration of carbon dioxide in the atmosphere has increased by close to 30% since the start of the Industrial Revolution.
Random Events
These include asteroid or comet collisions, nearby supernovas, and a gamma-ray burster pointing at the solar system. It might include unforeseen technological events causing massive environmental degradation, the rearrangement of the Earth's surface, and the extinction of the human species All of which are unpredictable and, obviously, do not follow any long-term trends which is a useful for any reasonable futurological exercise.
Geodynamics
The following geological events will occur in the relative near fture compared to your hundreds of megayears timescale. But hey give an indication of what a dynamic geological system can produce over sufficiently long timescales.
Tectonics-based events will continue to occur well into the future and the surface will be steadily reshaped by tectonic uplift, extrusions, and erosion. Mount Vesuvius can be expected to erupt about 40 times over the next 1,000 years. During the same period, about five to seven earthquakes of magnitude 8 or greater should occur along the San Andreas Fault, while about 50 magnitude 9 events may be expected worldwide. Mauna Loa should experience about 200 eruptions over the next 1,000 years, and the Old Faithful Geyser will likely cease to operate. The Niagara Falls will continue to retreat upstream, reaching Buffalo in about 30,000–50,000 years.[9]
In 10,000 years, the post-glacial rebound of the Baltic Sea will have
reduced the depth by about 90 m (300 ft). The Hudson Bay will decrease
in depth by 100 m over the same period.[30] After 100,000 years, the
island of Hawaii will have shifted about 9 km (5.6 mi) to the
northwest. The planet may be entering another glacial period by this
time.
Continental Drift
This is driven a combination of subduction and the presence of a hydrosphere (a fancy way of says Earth has seas and oceans on its surface). The arrangement of land masses progressively undergoes change. The longer the timescale the more massive this changes will be.
At present, the continents of North and South America are moving
westward from Africa and Europe. Researchers have produced several
scenarios about how this will continue in the future.[46] These
geodynamic models can be distinguished by the subduction flux, whereby
the oceanic crust moves under a continent. In the introversion model,
the younger, interior, Atlantic ocean becomes preferentially subducted
and the current migration of North and South America is reversed. In
the extroversion model, the older, exterior, Pacific ocean remains
preferentially subducted and North and South America migrate toward
eastern Asia.[47][48]
As the understanding of geodynamics improves, these models will be
subject to revision. In 2008, for example, a computer simulation was
used to predict that a reorganization of the mantle convection will
occur over the next 100 million years, causing a supercontinent
composed of Africa, Eurasia, Australia, Antarctica and South America
to form around Antarctica.
The above image of Pangea Ultima a predicted future super-continent.
50 million years from now the Mediterranean sea may vanish and the collision between Europe and Africa will create a long mountain range extending to the current location of the Persian Gulf. Australia will merge with Indonesia, and Baja California will slide northward along the coast. New subduction zones may appear off the eastern coast of North and South America, and mountain chains will form along those coastlines. To the south, the migration of Antarctica to the north will cause all of its ice sheets to melt. This, along with the melting of the Greenland ice sheets, will raise the average ocean level by 90 m (300 ft). The inland flooding of the continents will result in climate changes.[46]
As this scenario continues, by 100 million years from the present the
continental spreading will have reached its maximum extent and the
continents will then begin to coalesce. In 250 million years, North
America will collide with Africa while South America will wrap around
the southern tip of Africa. The result will be the formation of a new
supercontinent (sometimes called Pangaea Ultima), with the Pacific
Ocean stretching across half the planet. The continent of Antarctica
will reverse direction and return to the South Pole, building up a new
ice cap.
This based on one of three models for the formation of a future super-continent (in this case the introversion model).
The subduction flux model led to this possible future supercontinent
a computer simulation was used to predict that a reorganization of the mantle convection will occur over the next 100 million years, causing a supercontinent composed of Africa, Eurasia, Australia, Antarctica and South America to form around Antarctica.
While the extroversion model of continental drift gave this future.
predicted that the continents of North and South America would continue to advance across the Pacific Ocean, pivoting about Siberia until they begin to merge with Asia. He dubbed the resulting supercontinent, Amasia.[52][53] Later, in the 1990s, Roy Livermore calculated a similar scenario. He predicted that Antarctica would start to migrate northward, and east Africa and Madagascar would move across the Indian Ocean to collide with Asia.[54]
In an extroversion model, the closure of the Pacific Ocean would be
complete in about 350 million years.[55] This marks the completion of
the current supercontinent cycle, wherein the continents split apart
and then rejoin each other about every 400–500 million years.[56] Once
the supercontinent is built, plate tectonics may enter a period of
inactivity as the rate of subduction drops by an order of magnitude.
This period of stability could cause an increase in the mantle
temperature at the rate of 30–100 °C (54–180 °F) every 100 million
years, which is the minimum lifetime of past supercontinents. As a
consequence, volcanic activity may increase
The formation of a supercontinent will be main event that will sahpe the face of the Earth. Since there are three models of continental drift each predicting their own version of a future supercontinent the only recommendation that can be made to the OP is choose the one that suits your story best and go with it.
The general changes to planet Earth over next few hundreds of millions of years which impact on life on the planet and which will influence factors concerning its cartography. many of which need to be taken into account with respect to their impact on any human inhabitants.
Over time intervals of hundreds of millions of years, random celestial events pose a global risk to the biosphere, which can result in mass extinctions. These include impacts by comets or asteroids with diameters of 5–10 km (3.1–6.2 mi) or more, and the possibility of a massive stellar explosion, called a supernova, within a 100-light-year radius of the Sun, called a Near-Earth supernova. Other large-scale geological events are more predictable. If the long-term effects of global warming are disregarded, Milankovitch theory predicts that the planet will continue to undergo glacial periods at least until the Quaternary glaciation comes to an end. These periods are caused by eccentricity, axial tilt, and precession of the Earth's orbit.[10] As part of the ongoing supercontinent cycle, plate tectonics will probably result in a supercontinent in 250–350 million years.
