Beyond R2: The Role of Polynomial Degree in Modeling External Temperature and Its Impact on Heat-Pump Energy Demand

Missing values in hourly outdoor air temperature series are common and can bias building energy assessments that rely on uninterrupted temperature profiles. This paper examines how the polynomial degree can be used to reconstruct incomplete temperature data from the duration curve, which affect the energy indicators of an air-source heat pump (ASHP). Using an operational dataset from Opole, Poland (1 September 2019–31 August 2020; 5.1% gaps), global polynomials of degree n = 3…11 were fitted to the sorted hourly temperatures, and the reconstructions were mapped back to time. The reconstructions drive a building–ASHP model evaluated for two supply-water regimes (LWT, leaving water temperature = 35 °C and 45 °C). Accuracy is assessed with mean absolute error (MAE), root-mean-square error (RMSE), and R2 on observed, filled, and full subsets—including cold/hot tails—and propagated to energy metrics: seasonal space-heating demand (Qseason); electricity use (Eel); seasonal coefficient of performance (SCOP); peak electrical power (Pel,max); seasonal minimum coefficient of performance (COPmin); and the share of error due to filled hours (WFEfill). All degrees satisfy . For LWT = 35 °C, relative changes span ≈ −2.22…−1.63% and ≈ −21.6…−7.7%, with ≈ +0.53…+0.80%. For LWT = 45 °C, remains ≈ −0.43% across degrees. A multi-criterion selection (seasonal bias, stability of energy indicators, tail errors, and WFEfill) identifies n = 7 as the lowest sufficient degree: increasing n beyond seven yields negligible improvements while raising the overfitting risk. The proposed, data-driven procedure makes degree selection transparent and reproducible for gap-filled temperature inputs in ASHP studies.