Precipitation strengthening in titanium-stabilized austenitic stainless steels can improve the hot yield strength, as requested, e.g., for nuclear industry applications. The resulting properties depend mainly on the parameters of the heat treatment and previous forming. The influence of the heat treatment parameters on the development of the microstructure and mechanical properties was determined for steel 08Ch18N10T (GOST). Solution annealing and stabilization with different temperatures and holds were performed on the steel, which was, in delivered condition, stabilized at 720 °C. Heat-treated samples were subjected to static tensile testing at room temperature and at 350 °C, microstructural analysis using light, scanning electron and transmission electron microscopy focused on precipitates, and HV10 hardness testing. The strengthening mechanism and its dependence on the stabilization parameters are described. The results of the experiment show the influence of the state of the input material on the final effect of heat treatment—repeated heat treatment achieved lower-strength characteristics than the initial state, while almost all modes showed above-limit values for the mechanical properties. Stabilization temperatures of 720 to 800 °C were found to be optimal in terms of the achieved hot yield strength. At higher temperatures, slightly lower strengths were achieved, but at significantly shorter dwell times.