The analysis of an inclined plane heat source moving along the surface of a semi-infinite solid is presented. Material passing by the heat source is eliminated from the analysis to simulate its removal by an orthogonal cutting process. The solution, expressed in terms of dimensionless parameters, is obtained by solving the heat equation numerically with the finite element method for a wide range of cutting conditions. The solution is used to evaluate shear plane temperatures in orthogonal machining and grinding zone temperatures in conventional and creep feed grinding.