These conditions seem rather restrictive. If we imagine our Ising spins living on the atoms of a crystal lattice, with interaction strength J depending on the distance between adjacent atoms (to have coupling), the heat bath of the canonical Ising model is naturally interpreted, I suppose, as the mechanical degrees of freedom of the lattice (and the mechanical energy thereof as "heat"), which are not that many wrt the number of spins, and not necessarily ergodic, if the crystal is harmonic for instance.