In this work, three melt-pouring temperatures (1450 °C, 1480 °C, 1520 °C) and CoAl2O4 inoculant contents in the shell mold’s primary coating (0 wt%, 5 wt%, and 10 wt%) were selected to study microstructural and mechanical property changes of the Inconel 713C® nickel-based superalloy. The castings’ phase transformation temperatures, phase constitution, microstructure, and mechanical properties at room and elevated temperatures were investigated via thermodynamical simulations, differential thermal analysis, light and scanning electron microscopy, energy-dispersive X-ray spectroscopy, and tensile and stress-rupture tests. The pouring temperature and inoculant content strongly influenced the mean equiaxed grain size, which ranged between 2.36 and 6.55 mm. The primary microstructure of Inconel 713C® castings, owing to its complex chemical composition, comprised multiple phases, including γ, γ’, MC, M3B2, and Ni7Zr2. The mean size of γ’ was in the 0.446–0.613 μm range, depending on the casting variant. Grain refinement with CoAl2O4 at ambient temperature for each melt-pouring temperature led to increased yield strength (YS) and ultimate tensile strength (UTS). YS was in the range of 775–835 MPa, while UTS was in the range of 868–1010 MPa. A reverse trend was observed in samples that crept in 982 °C/152 MPa, while for each variant, the time to rupture exceeded 30 h. The maximum time to rupture was 46.1 h obtained in the unmodified casting poured at 1480 °C.