A comparison between two quasi-steady state models describing a three dimensional conductive thermal field inside a brick-type solid under a moving laser heat source with a Gaussian profile is carried out. One of the two model has been simplified by neglecting the thermal diffusion along the direction of the motion. This model is suitable for high values of the Peclet number. The thermophysical properties of the solid are temperature dependent and radiative and convective heat losses, the latter due to an impinging gas jet on the upper surface, have been taken into account. The comparison has been made in terms of temperature profiles, maximum temperature ratios and temperature fields. The differences between the two models are around 35% for Reynolds numbers greater than 10000 and for Pe = 0.1. The influence of the width of the solid is weak for Reynolds number greater than 10000. Relative errors are less than 5% for Pe ≥ 1 and they are negligible for Pe ≥ 5 for all the parameter ranges considered in this paper.