Heat transfer in the thermal boundary layer beneath a generalized vortex flow has been considered. The steadily revolving flow is allowed to vary with the distance r from the symmetry axis as r(m). The governing equations for heat and momentum transport transformed exactly to a coupled set of ordinary differential equations by means of a tailor-made similarity transformation. Some different flow situations in presence of suction have been considered, including solid-body rotation (m = +1) and a potential vortex (m = -1). The thermal boundary layer was observed to thicken monotonically with decreasing m-values, accompanied by a reduction of the heat transfer rate through the planar surface above which the flow revolves. These findings were explained as the combined influence of two different effects, namely: (i) a variation of the effective Prandtl number (m + 3)Pr/2 that directly affected the thermal diffusion, whereas (ii) an indirect variation of the axial velocity component affected the thermal convection. (C) 2017 Elsevier Ltd. All rights reserved.