  We study the thermal insulation of a bounded body
$\Omega\subset\mathbb{R}^n$, under a prescribed heat source $f>0$, via a bulk
layer of insulating material. We consider a model of heat transfer between the
insulated body and the environment determined by convection; this corresponds
to Robin boundary conditions on the free boundary of the layer. We show that a
minimal configuration exists and that it satisfies uniform density estimates.
