Comments: 21 pages, 1 figure, to appear in proceedings of the 10th International Symposium on Lattice Field Theory and Gravitation, October 8-12, 2017, Moscow, Russia

In this letter, we show that for any theory of gravity, a zero-temperature theory and a two-temperature theory of gravity agree on a massless two-loop effective action. We extend the old result on the massless massless two-temperature theory of gravity by a finite mass of the field.