Extensive numerical experiments were carried out to study the effect of cylinder heating on the characteristics of the flow and heat transfer in a two-dimensional horizontal laminar flow of air past a heated circular cylinder for the range of Reynolds numbers 0.001≤Re≤170. The fluid was treated as incompressible (density is independent of the pressure) while the variation of the fluid properties with temperature was taken into account. By including the transient density term of the continuity equation, which was neglected in a previous study by Lange, Durst, and Breuer [Int. J. Heat Mass Transfer 41, 3409 (1998)], we were able to predict correctly the vortex shedding frequency at various overheat ratios using an incompressible flow solver. The effect of dynamic viscosity and density variations on the flow dynamics occurring with the cylinder heating was analyzed separately. Another emphasis of the work was to investigate the physical mechanism behind the "effective Reynolds number" concept widely applied in engineering correlations. Similarity was discovered for the distribution of the local dimensionless viscous force, the vorticity and the Nusselt number at the cylinder surface and the pressure force in the rear part of the cylinder. Two characteristic temperatures, T eff=T∞+0.28(TW-T∞) for the flow dynamics and Tf=T∞+0.5(TW-T ∞) for the heat transfer, were identified.