In service-power engineering and aviation, gas-turbine engine structures are operated at elevated temperatures and under extensive variable mechanical loading, which is classified as thermomechanical fatigue (TMF). This coupling effect leads to flaw initiation and growth in components fabricated from thermally resistant nickel-based alloys. This paper presents experimental crack-growth data for isothermal pure fatigue, in-phase and out-of-phase TMF conditions. A crack-growth testing method is developed using inductive heating/forced convective cooling and direct crack-tip opening displacement techniques. The crack-growth experimental results are interpreted based on finite element analyses of the stress–strain rate fields at the crack tip under TMF conditions. Therefore, multi-physics numerical calculations are employed for the interaction of the heat loss from magnetic-field eddy currents with forced convective air cooling through a computer fluid dynamics model, which presents a nonuniform mechanical elastic–plastic stress distribution. Consequently, the dependence of the new nonlinear stress intensity factors on the crack length are obtained for each of the isothermal and thermomechanical cyclic deformation conditions. The polycrystalline XH73M nickel-based alloy tests performed show that, from the crack-growth acceleration viewpoint, the following order of arrangement of fatigue fracture diagrams is formed: isothermal pure fatigue, in-phase TMF, out-of-phase TMF, and isothermal pure fatigue at T = 400 °C and T = 23 °C. The differences and corresponding conclusions based on the interpretation of the experimental results of the crack growth rate characteristics at elevated temperatures in terms of elastic and nonlinear fracture resistance parameters are discussed.