Abstract This work applies Constructal design to study numerically the geometry of cavities bathed by a fluid with constant heat transfer coefficient that are intruded into a cylindrical solid body. The objective is to minimize the maximum excess of temperature between the solid body and the ambient by morphing the cavity geometry. Internal heat generating is distributed uniformly into the solid body which has adiabatic conditions on the outer surfaces. The total volume and the volume of the cavities are fixed. The cavities are rectangular with variable aspect ratio. The optimized geometry and performance are reported as functions of the ratio between the volume of the cavities and the total volume, the number of cavities and the dimensionless parameter that accounts for the convective heat transfer, λ . The main results indicate that for fixed number of cavities, ϕ c , and dimensionless parameter λ , there is an optimal number of cavities, N o , that minimizes the maximum excess of temperature and this optimal number of cavities in general increases as ϕ c and λ increases.