If plate tectonics stopped, the continents would stay in place rather than moving slowly around the face of the earth. This would also result in a reduction in volcanic activity and earthquakes. Lower volcanic activity causes warmer surface temperatures because particles released by volcanoes have a cooling effect.
Recent research into plate tectonics suggests that there were times during the earth's geologic history when the continental plates stopped moving. The motion of tectonic plates contributes to the cooling of the earth's interior. Thus, if plate tectonics were to stop, the earth would cool more slowly. Investigations of the isotopes present in older rocks on the earth suggests that this occurred roughly 1.5 billion years ago and may happen again.