We discuss population imbalances between different orbital states due to applied thermal gradients. This purely thermoelectric effect appears quite generically in nanostructures with a pseudospin (orbital) degree of freedom. We define an orbital Seebeck coefficient that characterizes the induced orbital bias generated across a quantum conductor in response to a temperature difference applied to the attached reservoirs. We analyze a two-terminal strongly interacting quantum dot with two orbital states and find that the orbital thermopower acts as an excellent tool to describe the crossover between SU(4) and SU(2) Kondo states. Our conclusions are reinforced with a detailed comparison to the charge thermopower using exact numerical renormalization group calculations.