  We discuss a relativistic model for heat conduction, building on a convective
variational approach to multi-fluid systems where the entropy is treated as a
distinct dynamical entity. We demonstrate how this approach leads to a
relativistic version of the Cattaneo equation, encoding the finite thermal
relaxation time that is required to satisfy causality. We also show that the
model naturally includes the non-equilibrium Gibbs relation that is a key
ingredient in most approaches to extended thermodynamics. Focussing on the pure
heat conduction problem, we compare the variational results to the second-order
model developed by Israel and Stewart. The comparison shows that, despite the
very different philosophies behind the two approaches, the two models are
equivalent at first order deviations from thermal equilibrium. Finally, we
complete the picture by working out the non-relativistic limit of our results,
making contact with recent work in that regime.
