Model predictive control has demonstrated strong supervisory value in building heat pump systems. However, its practical deployment remains constrained by a solver-dependent downstream decision layer that must solve a mixed-integer nonlinear program at every control update, thereby introducing non-deterministic runtime, convergence failure, and fallback events that are difficult to accommodate on resource-limited building automation hardware. This study proposes solver-free predictive supervisory control via thermal-potential part-load similarity decision mapping for a renewable multi-heat-source heat pump system with thermal energy storage. The proposed architecture isolates and replaces only the solver-dependent downstream decision layer of conventional MPC while preserving the full upstream predictive structure of disturbance forecasting, horizon-based thermal-potential computation, and demand shaping. Its key design mechanism is the definition of a capacity-referenced FCU-side thermal-potential demand coordinate and a TES-side regulation-residual coordinate relative to the predicted full-load heat pump thermal capacity, thereby forming a two-dimensional decision map with consistent command interpretation across seasonal operating conditions without condition-specific recalibration. Under identical predictive layers, look-back-generated forecast inputs, constraints, horizons, and actuation grids, the proposed architecture achieved 51.4% annual net electricity savings relative to the rule-based baseline, comparable to the 50.8% achieved by optimization-based MPC, while maintaining comparable room-temperature regulation, with seasonal RMSE remaining within 0.8–0.9 °C. More importantly, it reduced per-update computation time by approximately 1,000–2,500 times and eliminated solver fallback events across all tested configurations, whereas MPC incurred fallback events under every tested configuration. These results were obtained using a TRNSYS-validated standalone Python digital twin of the field-demonstrated PVT–GHX multi-heat-source heat pump system with TES, with annual relative errors of 2.0% or less across major energy terms. Overall, the results indicate that the solver-dependent downstream decision layer, rather than the shared upstream predictive structure, is the principal deployment bottleneck, and that thermal-potential part-load similarity decision mapping can retain MPC-grade supervisory performance while guaranteeing deterministic bounded execution.