Numerical solutions have been carried out to determine the temperature distribution along the exposed surface of a convectively cooled wall whose rear side is heated by a periodic array of groove-embedded heating elements. The accuracy of the numerical procedure was verified by using it to solve a related problem in which the heating occurs at discrete surface patches and then comparing those results with an exact solution. The numerical results for the exposed-surface temperature distributions corresponding to groove and patch heating were compared, and remarkably close agreement was found to prevail. This finding suggests that the computationally convenient exact solution for patch heating can be employed to obtain results for groove heating. The parameters which affect the uniformity of the temperature distribution on the convectively active surface were identified, and their quantitative influence was explored.