This paper is a proposal to embed tree-shaped vasculatures in a wall designed such that the wall withstands without excessive hot spots and peak stresses the intense heating and pressure that impinge on it. The vasculature is a quilt of square-shaped panels, each panel having a tree vasculature that connects the center with the perimeter. The vascular designs for volumetric cooling can be complemented by the shaping and distributing of channels for maximum strength and thermal performance at the same time. Numerical simulations of heat flow and thermal stresses in three directions show that it is possible to determine the optimal geometric features of configurations with radial channels and trees with radial and one level of bifurcations. The global performance is evaluated in terms of the overall thermal resistance and peak von Mises stresses. The dendritic design is superior under the studied thermal condition.