Buildings are complex assets with evolving uses, variable occupancies, and long-life cycles that drive high operational costs and substantial energy demand. Globally, they account for roughly 30–40% of greenhouse-gas emissions, making accurate short-term forecasting crucial to reduce both economic and environmental impacts. While Machine Learning (ML) is increasingly adopted, purely data-driven models often require large datasets and may violate physical constraints—especially in data-scarce contexts. This work proposes a hybrid predictive framework that couples Physics-Informed Neural Networks (PINNs) with dynamic energy simulation and energy-balance constraints to forecast, one hour ahead, indoor operative temperature (To) and cooling electricity (Eel,Cool) in a Multi-Storey Residential Building in Southern Italy. The PINN operates in two phases: Phase I predicts To,t+1 and then estimates Eel,Cool,t+1, embedding thermodynamic consistency into the loss to reduce reliance on computationally expensive simulations and deliver physically plausible predictions. On the test set, the PINN attains 0.265℃ RMSE for To (CVRMSE = 0.98%, MBE = −0.002℃, NMBE = −0.01%) and 0.185 kWh RMSE for Eel,Cool (CVRMSE = 13.10%, MBE = 0.066 kW, NMBE = 4.65%). Benchmarked against established ML baselines, MLP, Random Forest, and Linear Regression, trained with identical preprocessing and splits, the PINN delivers sub-0.3℃ temperature errors and reduces energy RMSE by 66–81% relative to the best baselines. These results demonstrate that PINNs can bridge data scarcity and physical interpretability, enabling robust one-hour-ahead forecasts that support proactive control towards sustainability targets.