> some kind of energy
The negenergy (negative energy) here is just the (unnormalised, hence the 1/Z term) log-probability mass or density. Like the logit outputs of classifier.
You shouldn't read anything more into the 'energy'. There is no temperature parameter in these minimax models (although adding one to smooth the model during sampling or learning can be useful, to interpolate between pure noise and the learnt model).
For what it's worth there is a parameter in front that functions as a kind of temperature, except there's more than one parameter so it's not an exact translation. You can still reason about it somewhat (or split it up into a single temperature times a convex combination of hamiltonians).
But there's one setting in which the energy E(x) = Σ_j λ_j H_j(x) really does become a physical (physics-esque) energy: if you sample from the distribution using Hamiltonian Monte Carlo (an MCMC algorithm). Then E(x) is the potential energy of a sample/particle at position x, which is also given a kinetic energy K with the sume E+K held constant as the particle moves about to explore the distribution. It's a cool algorithm but after having used it I'm still not sure how useful it is.
It is indeed quite cool how it works.