  We are interested in the thermal insulation of a bounded open set $\Omega$
surrounded by a set whose thickness is locally described by $\varepsilon h$,
where $h$ is a non-negative function defined on the boundary $\partial\Omega$.
We study the problem in the limit for $\varepsilon$ going to zero using a
first-order asymptotic development by $\Gamma$-convergence.
