I think the title sums up pretty well my doubts. I learned QFT from Peskin and Schroeder and other common sources, all implicitly defined QFT at zero temperature. Then I started learning about lattice QCD, how to define the action, how to find continuum limits, the importance of the dependence of coupling constant with lattice spacing etc. So far so good. We want to do our calculations on the lattice but keeping in mind the continuum limit is where the original model is, so we want to lower g as much as possible, or increase beta, or whatever you call these variables. But as I read articles on the subject I kept encountering this statistical mechanical terminology all over the place. In particular, finite-temperature phase transitions. So I kept digging and learned that there is this whole world of physics of finite temperature QFT. This is new to me but I think I understand the gist of it, but what bothers me is that it seems to be related to lattice formulation but not in an obvious way. Like a phase transition far from the continuum limit interpreted as a finite temperature phase transition. It seems to imply temperature and coupling constant are the same thing, which doesn't sound right at all. On the other hand, I've seen people talk about lattice formulation of finite temperature QCD, which sounds like confirmation that these are completely different things. I'm a little confused and overwhelmed. Any light on this subject would be greatly appreciated.