  We calculate the thermal conductance $G^T$ of diffusive Andreev
interferometers, which are hybrid loops with one superconducting arm and one
normal-metal arm. The presence of the superconductor suppresses $G^T$; however,
unlike a conventional superconductor, $G^T/G^T_N$ does not vanish as the
temperature $T\to0$, but saturates at a finite value that depends on the
resistance of the normal-superconducting interfaces, and their distance from
the path of the temperature gradient. The reduction of $G^T$ is determined
primarily by the suppression of the density of states in the proximity-coupled
normal metal along the path of the temperature gradient. $G^T$ is also a
strongly nonlinear function of the thermal current, as found in recent
experiments.
