We study the connection between the spin-heat and spin-charge response in a disordered Fermi gas with spin-orbit coupling. It is shown that the ratio between the above responses can be expressed as the thermopower S=−(πkB)2Tσ′/3eσ times a number Rs which depends on the strength and type of the spin-orbit couplings considered. The general results are illustrated by examining different two-dimensional electron or hole systems with different and competing spin-orbit mechanisms, and we conclude that a metallic system could prove much more efficient as a heat-to-spin than as a heat-to-charge converter.