Deep sea vents were discovered when I was in my 20's before that we used to think abiogenesis had something to do with lightning hitting a mud puddle. The evidence that life formed around such vets on Earth is strong but inconclusive. Fatty acids from clay in the vent spontaneously form primitive cell membranes (in vents and mud puddles). Sulphur provides chemical energy, porous rock around the vent provides a sponge like scaffold for life to take root and extract passing nutrients. Most importantly the vents are predictable, the deep, still water stabilizes the temperature gradient. Convection currents cycle the fatty cells through the gradient allowing different chemical reactions within the membrane to synchronize themselves to the thermal cycle (much the same as plants match the cycle of night and day). If that really is how life got started then it's likely that primitive cells are still being spontaneously created near these vents today, the practical problem for scientists researching this idea is finding them before evolved life such as shrimp eat them..
Yeah, all this makes sense, but all you're describing is really what I meant with those "more predictable pathways". It's not like the life forms living around those vents are just bathing in the heat and having it fuel various endothermic reactions, which is what I understood by the mention of "more free energy around [in high-temperature environment]". Surely this can help some things, but it can be as easily destructive as it can be constructive. Heating a soup of chemicals can eventually give you a lot of interesting other chemicals, but for organized, self-replicating systems, that's not the major issue.
Well, a hydrothermal vent is VERY predictable - and STEADY.
Yes, but those life forms aren't working like thermocouplers, are they? They're still not working along the lines of "let's just inject a lot of heat into a living organism and see what random stuff happens". They're just carefully digesting some of the products of reactions occurring nearby.