  We study the Yang-Mills theory and quantum gravity at finite temperature, in
the presence of Lagrange multiplier fields. These restrict the path integrals
to field configurations which obey the classical equations of motion. This has
the effect of doubling the usual one--loop thermal contributions and of
suppressing all radiative corrections at higher loop order. Such theories are
renormalizable at all temperatures. Some consequences of this result in quantum
gravity are briefly examined.
