This paper reports the design study performed on a heat conduction panel having several heat sources at separate locations and a heat sink on one of the panel corners. The panel is given a thickness distribution so as to provide spatially varying heat conduction paths from the heat sources to the heat sink. The objective of thickness distribution design is to reduce the variation among heat source temperatures and the maximum heat source temperature simultaneously. The genetic algorithm is used to search for an optimum thickness distribution. The problem is a generic representation of the situations that are becoming common in a compact electronic equipment.