Abstract.The temperature fields of rotating laminar flows over a flat surface are investigated. Dissipation is considered, whereas free convection effects are neglected. The calculation is based on the knowledge of the flow fields, which have been studied in previous papers by the authors. In these papers first order approximations reduce the Navier-Stokes equations to ordinary differential equations. The basic ideas of this method are applied to the energy equation. In the special case of negligible dissipation the heat transfer of von Karman type flows can be compared with existing experimental data. The agreement is satisfactory.1. Introduction. The solution of a convective heat transfer problem is closely connected with the knowledge of the associated fluid motion since both the temperature distribution and the velocity field interact mutually. This dependence is only unilateral for an incompressible fluid with constant viscosity because the temperature distribution does not influence the flow field. For this reason solutions of the equations of motion, which are known from other investigations, can be used in order to obtain solutions of the associated heat transfer problems.In recent papers [1, 2] the authors have studied rotating flows over a flat surface by means of local first order approximations of the Navier-Stokes equations. Numerical results have been computed for the vortex flow normal to a flat surface, for the rotating disk in a fluid at rest (von Karman problem), and for the solid-body rotation of a fluid over a fixed flat plate (Bodewadt problem).In this paper the basic ideas of the new method are applied to the temperature fields of the above mentioned flows. Numerical solutions are presented for all problems.2. Basic equations. For a steady, axisymmetric, and laminar flow the NavierStokes equations, the equation of continuity, and the energy equation, in cylindrical coordinates (r, tp, z), are