  For a given balanced distribution of heat sources and sinks, $Q$, we find an
optimal conductivity tensor field, $\hat C$, minimizing the thermal compliance.
We present $\hat C$ in a rather explicit form in terms of the datum. Our
solution is in a cone of non-negative tensor-valued finite Borel measures. We
present a series of examples with explicit solutions.49J20, %Singular parabolic
equations secondary: 49K20, 80M50
