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Abstract: We are interested in the thermal insulation of a body Ω surrounded by a bulk layer Σ of insulating material. We consider a Robin boundary condition on the boundary of Σ that does not touch Ω; this corresponds to a model of heat transfer between the insulated body and the environment determined by convection. We will address the problem of proving the existence of an optimal Σ, and we will study a way to approximate the problem via first-order asymptotic development by Γ-convergence.