A theoretical analysis was made of steady-state temperature and heat flow anomalies in the earth's crust caused by contrasts in heat production and thermal conductivity. Exact expressions were derived for the temperature and heat flow anomalies caused by polygonal prism heat sources in a half space overlain by a layer of contrasting conductivity. Expressions were also developed for the approximate thermal effects of polygonal prisms of contrasting conductivity. A comparison was made between the exact and approximate heat flow over an infinite semicircular cylinder of contrasting conductivity. The two heat flow fields agree to within 5% for conductivity radios (the ratio of the conductivity of the medium and the conductivity of the cylinder) which are between 0.25 and 1.5. Comparisons were also made between polygonal prism and finite difference models, three-dimensional and one-dimensional models, and half space and two-layered half space models.

To illustrate the interpretation of heat flow anomalies a heat flow model was prepared for the Rolesville batholith and Castalia pluton, in Nash and Franklin Counties, North Carolina. It was shown that the observed variation in surface heat flow over these two granitic intrusions can be explained by variations in the thickness of the granite from 1 km to 30 km.