Consideration is given to the effects of mutual irradiation occurring between a fin and its adjoining base surfaces. The first part of the analysis deals with black surfaces. It is found that in the range of practical operating conditions, the fin heat loss is significantly reduced by the presence of the base surfaces. Additionally, the base surface heat loss may comprise an important part of the total heat loss from the system. In the second part of the paper, the formulation is extended to include selectively gray surfaces and arbitrary irradiation from external sources. This degree of generality leads to a complex mathematical system composed of several integral equations and a differential equation.