Metal Additive Manufacturing and Laser Powder Bed Fusion (LPBF), in particular, have come forth in recent years as an outstanding innovative manufacturing approach. The LPBF process is notably characterized by very high solidification and cooling rates, as well as repeated abrupt heating and cooling cycles, which generate the build-up of anisotropic microstructure and residual stresses. Post-processing stress-relieving heat treatments at elevated temperatures are often required in order to release some of these stresses. The effects of 1 h–hold heat treatments at different specific temperatures (solutionizing, annealing, stress-relieve and low-temperature stress-relieve) on residual stress levels together with microstructure characterization were therefore investigated for the popular Alloy 625 produced by LPBF. The build-up of residual stress is accommodated by the formation of dislocations that produce local crystallographic misorientation within grains. Electron backscattered diffraction (EBSD) was used to investigate local misorientation by means of orientation imaging, thereby assessing misorientation or strain levels, in turn representing residual stress levels within the material. The heavily constrained as-built material was found to experience full recrystallization of equiaxed grains after solutionizing at 1150 °C, accompanied by significant drop of residual stress levels due to this grains reconfiguration. Heat treatments at lower temperatures however, even as high as the annealing temperature of 980 °C, were found to be insufficient to promote recrystallization though effective to some extent to release residual stress through apparently dislocations recovery. Average misorientation data obtained by EBSD were found valuable to evaluate qualitatively residual stress levels. The effects of the different heat treatments are discussed and suggest that the peculiar microstructure of alloys produced by LPBF can possibly be transformed to suit specific applications.