Two-dimensional numerical computations have been conducted to investigate combined forced and natural convection around a cylinder in a cross flow. Reynolds number, Re, ranged between 75 and 150. Rayleigh number, Ra, was changed from 0 to 7×105. Combined convective heat transfer characteristics cannot be expressed by a simple summation of forced and natural convective heat transfer characteristics. An abrupt decrease of mean Nusselt number, Num, is observed in transition from forced convection to natural convection. A hysteresis occurs in the transition region and Num has two different values which depend on initial conditions. This is attributed to subcritical bifurcation of flow behind the cylinder. Num is higher for unsteady flows than for stcady flow in such a transition region.