Conjugate heat transfer by forced convection over a vertical cylinder without heat generation has been a subject of many investigations in the recent past. In the present work, the radial heat conduction along with heat generation in a vertical cylinder is considered for analysis. The steady two-dimensional conduction equation for the heat generating cylinder and steady two-dimensional laminar boundary layer equations for the flowing fluid are solved simultaneously using a finite-difference scheme. Results are presented for a wide range of conduction-convection, heat generating parameters and length to diameter ratio for a specific fluid having Prandtl number 0.005. It is found that the radial temperature distribution in the boundary layer as well as the cylinder are remarkably significant especially with the inclusion of internal heat generation in the cylinder.