A model based on transport equations was numerically implemented by the finite volume method (FVM) in a computational code in order to simulate the influence of the heat input, base metal thickness and preheating temperature on the thermal evolution and the cooling rate during the welding of the low alloy ferritic steels T/P23 and T/P24. As a consequence, it was possible to evaluate qualitatively the microstructure at the heat affected zone (HAZ) of these steels when a single weld bead was deposited on their surface and calculate the maximum hardness reached at this region. Goldak`s double-ellipsoid heat source model for power density distribution was utilized in order to obtain a good estimate of the cooling rate and dimensions of the fusion zone (FZ). The results are discussed in light of previous work and good agreement between experimental and simulated results was verified.