A finite difference calculation of forced convective heat transfer from an oscillating cylinder is carried out using vorticity, stream function and temperature as the dependent variables. The non-dimensionalized vorticity transport and energy equations in a non-inertial frame attached to the cylinder, are solved in a rectangular grid, based on a log-polar coordinate system. The effects of cylinder oscillation in the in-line and transverse directions, on the time dependent average Nusselt number and the Nusselt number distribution on the cylinder surface are investigated for a Reynolds number of 200. Some of the numerical predictions are compared with experimental data available in the literature. In the case of the stationary cylinder, the average Nusselt number was found to oscillate at twice the natural shedding frequency. The heat transfer rate from the oscillating cylinder increases with the increasing velocity amplitude. In the case of transverse oscillation. the location of maximum local Nusselt number was found to oscillate between the upper and lower surface of the cylinder. Contour maps of vorticity, stream line and isotherms are presented and the physical aspects of the flow field are discussed.