There's an important aspect of my headworld involving volcanoes which I planned many years ago. Recently I revisited this concept to refine it further, only to run into a few questions that I've been struggling with. My geology knowledge is quite limited and I can't find much information on these matters online.
Basically, I have a creature species that has adapted to living in colonies settled inside craters of massive extinct volcanoes. The rough concept was that, although the environment around these volcanoes is extremely harsh with low temperatures and constant, powerful wind currents, the volcanoes still emanate enough heat to provide a good settlement for this species. The heat consistently melts down the accumulating snow at the top of the crater walls, then the water streams down and pools up inside the crater. These pools make for the colony's water source, and there are fissures/openings in the rock that allow for the water to stream out too. In some cases this even forms waterfalls outside.
I was wondering, is it plausible for completely extinct volcanoes to still emit heat in such ways? Some time ago I read about an extinct volcano that still has magma simmering in its chamber(link), while its own structure prevents an eruption from happening again. However, I'm not very knowledgeable on the details of these cases and couldn't find much information on how common that is.