Based on the constructal and entransy theories, a constructal study on a cylindrical heat source cooled by laminar flow is carried out by applying equivalent resistance minimization as the optimization objective. The effects of the cylindrical diameter and the heat transfer coefficient of the heat source on its heat transfer performance are analyzed. The results show that when the volume of the heat source is fixed, there is no optimal diameter that leads to the minimum equivalent resistance of the heat source. With a decrease in the diameter and an increase in the heat transfer coefficient of the heat source, the equivalent resistance decreases, and the global heat transfer performance of the heat source system improves. Additionally, the surface temperature of the cylindrical heat source increases gradually along the flow direction, while its surface heat transfer coefficient decreases. Our results can provide some theoretical guidelines for the constructal designs of heat sources.