The thermal convection for Herschel-Bulkley fluids in duct is studied, theoretically in the case of constant physical properties, and experimentally from wall temperature measurements. The results of the theoretical analysis show that the non-Newtonian correction depends on the flow behavior index n and on the Herschel-Bulkley number Hb. Velocity measurements for isothermal and heating situation, reveal the incidence of the imposed thermal field on the flow structure. It is characterized by an increase of shear rate at the wall, and of the size of the flowing plug. Temperature measurements permit the study of the local heat transfer. Finally a correlation is proposed taking into account the modification of the wall shear rate induced by the rheological properties, and the temperature dependent character of the fluid.