The present paper determines numerically the optimal geometric parameters for the maximal peripheral cooling of a two-dimensional rectangular solid body with internal heat generation. The objective is to maximize the thermal global conductance (i.e., minimize the hot spot temperature on the solid body) by using the minimal cooling space. The flow is conducted around the heated solid body by a sequence of channels of independent width , where . Each configuration is free to morph itself in two directions: (a) the number of cooling channels, and (b) the aspect ratio of the heated body . The numerical results show that a number of cooling channels greater than one (i.e., ) is profitable in terms of thermal performance when the heated body resembles a square (i.e., ). However when is free to vary, the thermal performance does not necessarily increase with the number of cooling channels. The paper also discusses the importance to allow each configuration to morph itself in multiple directions by comparing the thermal performance of similar configurations with different number of degrees of freedom. Scale analysis is used to verify the results obtained numerically for all the degrees of freedom considered. The numerical results agree with the scaling trends.