Conjugate heat transfer around a circular cylinder with heat source was numerically investigated. Both the forced convection of water and conduction of carbon-steel were involved in the present simulation. A finite element formulation based on SIMPLE type algorithm was adopted for solving the incompressible Navier-Stokes equations coupled with energy equation. A conduction heat transfer problem inside the cylinder was trivially coupled with forced convection around the cylinder by using the Galerkin formulation of energy equation. The proposed algorithm was verified by solving the benchmark problem of conjugate heat transfer inside a cavity having a centered body. The effect of the Reynolds number on the temperature distribution on the cylinder surface and the maximum temperature inside the cylinder was examined. It was shown that the maximum temperature decreased as Reynolds number increased and that the position of the maximum temperature moved from the center to the rear part of the cylinder till Re = 20 and then moved back toward the center beyond Re = 20 since the reverse flow around the rear part of the cylinder became stronger as the Reynolds number further increased. Lastly, the maximum temperature of the cylinder with rotation was higher than that of the fixed one and the position of the maximum temperature inside the cylinder depended on the position and the strength of the dead zone.