Regardless the cause of the volcanism, it has absolutely nothing to do with surface temperature. That only impacts the immediate surface of Earth and not in any way that would either prevent or stimulate the buildup of subsurface pressure and heat.

Since the Earth is losing more heat to space than is falling on it from the Sun, and that heat is coming up from below, the core is gradually cooling. But there is so much heat inside the Earth and the rate is so slow that our Sun will die before Earth's core cools enough to solidify.

The Volcanism of Earth has nothing to do with the surface temperature of the planet, it's all about geological processes where molten rock is forced to the surface of the planet under pressure.

Additionally, volcanism isn't confined to the Earth. Mars was once volcanic, Venus still is, as is the Jovian moon Io, the Saturnine moon Enceladus and the Neptunian moon Triton. These are examples of volcanism within our solar system. Except for Venus, all the other locations of volcanism in the solar system have very cold surface temperatures.

On Io,

Magma erupts onto the surface from vents on the floor of paterae or on the plains from fissures, producing inflated, compound lava flows similar to those seen at Kilauea in Hawaii

Whereas, Enceladus and Triton experience cryovolcanism, where ice and water are ejected under pressure.