The interpretation of some recent measurements of spin-dependent voltage for which the electric conduction does not play a role rises some new fundamental questions about the effects of spin-dependent heat currents. A two spin-channel model is proposed in order to describe the effect of out-of-equilibrium spin-dependent heat carriers in electric conductors and insulators. It is shown that thermal spin-accumulation can be generated by the heat currents only over an arbitrarily long distance for both electric conductors or electric insulators. The diffusion equations for thermal spin-accumulation are derived in both cases, and the principle of its detection based on Spin-Nernst effect is described.
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