It wasn't always the case that people believed in continental drift, German geologist and meteorologist Alfred Wegener's(1)  theory that parts of the Earth's crust slowly drift atop a liquid core.   He believed  200 million years ago there was once a gigantic supercontinent which he called Pangaea ("All-earth") which slowly moved apart.

Wegener’s theory of continental drift became commonly accepted when the driving forces for continental drift were discovered during the 50s and 60s: The enormous heat in the Earth’s core and Earth’s mantle generates the flow of rocks within the Earth’s mantle, a process similar to the movement of warm water in a cooking pot. This heat-driven mass transport by convection leads not only to plate movement on the Earth’s surface but also to drifting of the continents floating on the plates.

visit enchantedlearning.com
Visit enchantedlearning.com

A new hypothesis says drifting of the large tectonic plates and the superimposed continents is not only powered by the heat-driven convection processes in the Earth’s mantle, but rather retroacts on this internal driving processes. In doing so, the continents function as a 'thermal blanket', which leads to an accumulation of heat underneath, and which in turn can cause the break-up of the super-continents.

To date  there had been no realistic mathematical–physical theory describing the interaction between the convective movement in the Earths mantle and the continental drift but V. Trubitsin, M. Kaban und M. Rothacher from the Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences have now developed a numerical model(2), based on the current position of the continents, the structures of the Earth’s mantle obtained through geophysical measurements, and the current displacement rates on the surface.

Hence they were able to calculate the future position of the continents in hundreds of millions of years. 

tectonic evolution and continental drift in 120 million years
Distribution of the continents in 120 million years

They say that the enormous heat in the Earth’s interior does not generally lead to a chaotic mass transport within the Earth’s mantle. On the contrary, the continents influence the heat distribution within the Earth’s mantle and the associated convective mass flow. In other words the continents act as a thermal blanket causing heat to accumulate beneath. A self-regulating system develops, beginning and ending with a super-continent. This super-continent breaks apart due to heat accumulation which in turn leads to a reorganoization of mantle convection with the pieces ultimately joining again to form a large super-continent.

Obviously more heat in the thermal blanket could impact that, though it is unlikely something like  projected global warming would actually move mountains.  The graphic above is their projection of what the Earth will look like in 120 million years  - the good news is there won't be any more 3 day waits to get through the Panama Canal and Europe will have even easier access to cheap labor.  The bad news is Casablanca will be in Portsmouth.

NOTES:

(1) The Origin of Continents and Oceans, 1915

(2) V. Trubitsin, M. Kaban and M. Rothacher: “Mechanical and thermal effects of floating continents on the global mantle convection”, Physics of the Earth and Planetary Interiors (Vol. 171, S. 313-322).