Thermal instability of divertor plasma transport in steady-state operation is a critical issue in reactor design. Identifying the thermally stable regime is crucial for the successful operation of a fusion reactor. This study aims to explore the regime of stable operation for divertor plasma and to investigate how this stability depends on key engineering parameters. For this purpose, a linear stability analysis is applied to equilibrium solutions of the particle, momentum, and energy balance equations obtained from the core-SOL-divertor model, providing a novel application of point-model-based analysis. In this regard, this study specifically addresses plasma heat control via radiation within the divertor volume. While alternative heat exhaust strategies utilizing strong radiation localized near the X-point—such as the X-point radiator regime—are also highly important, they are outside the scope of this work. Under this framework, this study presents two main findings through model calculations for JT-60U and JA-DEMO. First, the divertor plasma exhibits three thermally stable states: low-recycling, high-recycling, and weakly detached, while the intermediate states between them are unstable. Within the context of the localized divertor-volume radiation, the weakly detached state is identified as the expected operational regime in future fusion reactors. Second, as initial examples demonstrating the capability of the stability analysis framework for future extensive parametric surveys, the stability of the weakly detached state is found to be primarily sensitive to the exhaust power; increasing power raises the lower temperature limit and significantly narrows the stable range. Variations in the major radius have little influence on stability, whereas a reduction in the minor radius slightly raises the lower stability limit within the parameter range examined. The proposed stability evaluation framework provides qualitative guidance for selecting reactor design parameters that expand the stable operational window of divertor plasmas.