If the asthenosphere cooled and stopped flowing how would you expect the movement of tectonic plates in the lithosphere to change?

Answer 1

The "continental drift" part of lithospheric plate tectonics would end. The lithospheric plates move around by one of two mechanisms: 1) they are conveyed (through friction) by movement of the underlying asthenosphere (this is a passive view of the lithosphere, in which mantle convection controls tectonic plate drift); and/or 2) they move around to fill in spaces created when dense lithosphere sinks (subducts) into the mantle (see ridge-push/slab-pull model). Geologists are still discussing the relative importance of each of these two mechanisms in driving plate tectonics. If the asthenosphere stopped flowing then mechanism 1 would end, as there'd be no movement to convey the lithosphere. For mechanism 2, if the asthenosphere stopped flowing, then it wouldn't be able to get out of the way to permit the dense parts of the lithosphere to subduct. When the asthenosphere ceases to flow, then heat from earth's interior would only escape through conduction, which is a less efficient process than convection. The heat would likely build until huge pools of magma (molten rock) develop and burn their way up through the asthenosphere and lithosphere, creating enormous volcanoes.