Conceivably there could be interactions which are sufficiently constrained to prevent the equipartition theorem from coming into play in practice. For example, an interaction with a massive carrier may not be able to support thermal transfer except at very high energies.

Gravitational heat transfer would, I assume, work for everything, but it would also be very very slow.

We're a little bit spoiled by EM - it makes thermal interactions happen quickly and at all energy scales.