Of concern is the thermal insulation ability of an anisotropic material (anisotropy means the thermal conductivity is direction-dependent). We propose to use the Dirichlet eigenvalues and eigenmodes, especially the principal ones, to measure the thermal insulation. More specifically, we propose to use the principal Dirichlet eigenvalue of the elliptic operator on the unit ball (occupied by the anisotropic material) as a simple thermal insulation measurement ; numerically we obtain some user-friendly formulas for this Dirichlet eigenvalue in terms of the trace and determinant of the thermal tensor. We also study the scenario of protecting a thermal conductor (e.g., a space shuttle) from overheating by coating it with an insulator. We establish and prove some easy-to-use rules for the optimal thickness of the coating. We achieve this by studying the behavior of Dirchlet and Robin eigenvalues and eigenfunctions, as well as the heat equation itself, in the singular limit as the coating thickness approaches 0.