Enhancement of natural convection heat transfer in an enclosure by a rotating cylinder is investigated numerically. A penalty finite-element method with a Newton-Raphson iteration algorithm is adopted to solve the governing equations with the boundary conditions, and the accuracy of solutions is sensitively affected by the grid system combining curve-sided and rectangular quadrilateral elements. Since the flow fields of fluids are induced by mutual interaction between the natural convection and the rotating cylinder, the contribution of the rotating cylinder to natural convection heat transfer depends on the direction of rotation of the cylinder. For the counter-clockwise rotating cylinder situation, the contribution is found to be substantial when the value of Gr/Re2 is larger than 100 : however, for the clockwise rotation cylinder situation, the contribution is hardly found even when the value of Gr/Re2 is equal to 1.