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The mathematical theory used in calculating temperatures of intrusions is reviewed, primarily from the point of view of finding temperatures in the country rock outside them. It is shown that the detailed behavior inside the intrusion, for example the mechanism of solidification and the possible effects of convection, becomes progressively less important as the distance from the contact increases, so that at distances of one-quarter of the thickness or more the simple theory of Lovering is adequate. The theory for sheets, stocks, laccoliths, and some irregularly shaped bodies is given, together with the effect of dissimilar thermal conductivities. The effects of latent heat, convection, and the circumstances of intrusion are discussed. Applications to metamorphism, rock magnetism, and argon loss caused by heating by intrusions are reviewed.