The quantitative understanding of the processes involving focused beams, such as recrystallization of semiconductors or thermal annealing and recording, requires a detailed knowledge of the temperature profiles within the target. We have derived first a normalized analytical representation for the distribution of power dissipation in targets bombarded with electron beams. This representation has then been combined with the Green’s function approach and Kirchoff transformation to predict the steady state and transient temperature profiles in targets with linear and nonlinear thermal conductivities. This calculation for the case of transient heating when thermal conductivity changes with temperature is not strictly accurate and, therefore, a numerical technique was developed involving successive over relaxation. Considerable care was needed in choosing the distribution of mesh size because of the great difference between beam radius (down to 2 μm) and target dimensions (250–500 μm). Numerical calculations for silicon (a nonlinear conductor) agreed well with transient analytical calculations using Kirchoff transformation.