Heating a cylinder should affect the flow pattern around it and the heat transfer from its surface. Numerical computation of the flow and related heat transfer has been carried out for a circular cylinder mounted in a channel flow for a free-forced combined convection regime. In the case that buoyancy assists the flow, the results showed that the transition from unsteady flow to steady flow occurred under different conditions depending on the Ri number, Re number and blockage ratio. With a constant Re number, the critical Ri number at which the transition occurs decreases with increasing blockage ratio, and with a constant Ri number, the transition Re number increases with the blockage ratio. In the case of negative buoyancy, on the other hand, the increase of the Ri number facilitates the growth of the length scale of the Karman vortices. The buoyancy effect on flow instability is less conspicuous compared with that in the above two cases in the case of horizontal flow, but local heat transfer characteristics are still changed by the buoyancy effects.