What will happen when the earth's core cools?

Inspired by this question

If there is still any form of humans or other intelligent social and technologically advanced species on earth as the core finally cools and plate tectonics begins to slow how do you think life will adapt? Once it finally comes to an end do you think life on this planet will die with it?

This is assuming the sun hasn’t already gone mental (I think they call it Red Giant) and fried us all by then.