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

Thermal gauge theories with Lagrange multiplier fields