This paper reports the sensitivity of the thermal and the displacement histories predicted by a finite element analysis to material properties and boundary conditions of a directed-energy deposition of a M4 high speed steel thin-wall part additively manufactured on a 42CrMo4 steel substrate. The model accuracy was assessed by comparing the simulation results with the experimental measurements such as evolving local temperatures and distortion of the substrate. The numerical results of thermal history were successfully correlated with the solidified microstructures measured by scanning electron microscope technique, explaining the non-uniform, cellular-type grains depending on the deposit layers. Laser power, thermal conductivity, and thermal capacity of deposit and substrate were considered in the sensitivity analysis in order to quantify the effect of their variations on the local thermal history, while Young’s modulus and yield stress variation effects were evaluated on the distortion response of the sample. The laser power showed the highest impact on the thermal history, then came the thermal capacity, then the conductivity. Considering distortion, variations of the Young’s modulus had a higher impact than the yield stress.