Heisenberg exchange interaction (sometimes called as magnetic stiffness?), originating from the Coulomb interaction and the Fermion statistics, is widely used in theories of magnetism. Conventionally, we don't consider its temperature dependence. I was just wondering if we could find any mechanism to incorporate the temperature effect.
I would say that "exchange interaction" is a loose term which does not make a proper definite answer to the question very easy. We can talk about Coulomb exchange, kinetic exchange, direct or double exchange etc... This being said, in all these mechanisms, the temperature dependence is driven by the statistics of the fermions, while the associated interactions (Coulomb interaction) or the Pauli exclusion principle, are temperature independent. For interesting insights into the intricacies of the exchange interactions, I would highly recommend the book chapter by Erik Koch, freely available here.