Well if you're doing fermionic thermal field theory sure (where the `integral' on Grassmann numbers is just some linear operation which satisfies certain proper

Well if you're doing fermionic thermal field theory sure (where the `integral' on Grassmann numbers is just some linear operation which satisfies certain properties). But apart from that I thought all the thermodynamic quantities were defined in terms of the partition function, which is a perfectly well-defined (Riemann) integral...