An analytical solution to the three-dimensional quasi-stationary problem in a finite depth and width solid with a circular Gaussian moving heat source at the body surface is developed and analyzed. The temperature distribution and the axial coordinate at which the maximum midplane temperature is achieved are presented as a function of Peclet number, solid thickness and width. The dependence of the maximum midplane temperature on the process parameters is highlighted. Combinations of process parameters for which the solution to the three-dimensional problem can be approximated by those to simpler models are pointed out.