Strengthening the heat-affected zone in actual weld joint of Inconel 625 alloys was crucial for engineering applications in aerospace, petroleum, nuclear energy, and marine industries. In this study, Gleeble thermal simulations were employed to investigate the influence of welding heat on grain morphology, carbide evolution, and mechanical properties of Inconel 625 alloys manufactured by selective laser melting (SLM). Typical elongated columnar grains along the building direction and parallel columnar array with obvious layer boundaries along the scanning direction were observed in SLM-processed Inconel 625 alloys with hot isostatic processing treatment. After Gleeble thermal simulations, the prominent equiaxed grains appeared in the entire gauge region that was directly exposed to the simulated welding heat owing to the recrystallization process. Meanwhile, the size of equiaxed grains significantly increased with the increasing peak temperature. Particularly, only MC-type carbides were observed in the γ-Ni matrix before and after the thermal simulation owing to the fairly rapid heating (100 °C/s) and cooling (30 °C/s) process. Simulated welding heat produced a negative effect on the mechanical properties of the Inconel 625 alloys, especially for the peak temperature of 1350 °C. Then, the respective contributions of the four conventional strengthening mechanisms were successfully quantified for understanding the effect of the simulated peak temperature on the yield strength of the Inconel 625 alloys. Finally, the observations of microstructural evolution indicated that the cross-slip of dislocations was the dominant deformation mechanism to account for the large strain-hardening rate of the Inconel 625 alloys.