The graviton self-energy at finite temperature depends on fourteen structure
functions. We show that, in the absence of tadpoles, the gauge invariance of
the effective action imposes three non-linear relations among these functions.
The consequences of such constraints, which must be satisfied by the thermal
graviton self-energy to all orders, are explicitly verified in general linear
gauges to one loop order.Comment: 4 pages, minor corrections of typo
