Wire + arc additive manufacturing (WAAM) is a versatile, low-cost, energy-efficient technology used in metal additive manufacturing. This WAAM process uses arc welding to melt a wire and form a three-dimensional (3D) object using a layer-by-layer stacking mechanism. In the present study, a Ni-based superalloy wire, i.e., Inconel 625, is melted and deposited additively through a cold metal transfer (CMT)-based WAAM process. The deposited specimens were heat-treated at 980 °C (the recommended temperature for stress-relief annealing) for 30, 60, and 120 min and then water quenched to investigate the effect of heat treatment on microstructure and phase transformation and to identify the optimum heat treatment condition. Microstructural results show that the heat treatment, in general, eliminates the brittle Laves phases regardless of the time without changing the grain morphology. However, an increment in the amount of the delta phase is observed with the longer heat treatment periods. Additionally, the size of MC (metal carbide) of Nb is also observed to increase with heat treatment time. This study provides an in-depth understanding of the correlation between heat treatment time and microstructure in additively manufactured Inconel 625, which can facilitate determining the optimum heat treatment condition in a later study.