Accurate parameterization of the photovoltaic single-diode model is usually obtained from complete current–voltage (I-V) measurements. However, full I-V curve tracing is not always available in real monitoring environments, where the most accessible variables are irradiance and module temperature. This paper proposes a hybrid methodology for reconstructing the five parameters of the single-diode model from irradiance and temperature data. The method first estimates the maximum-power point and the remaining remarkable points of the I-V curve as well as the photocurrent ($I_{ph}$) through regression models calibrated on measured data. These predicted points are sufficient to solve the SDM equation. A numerical approach is then used to identify the five SDM parameters while enforcing physical admissibility constraints. The method is validated using NREL outdoor datasets from three locations and several photovoltaic technologies. The results show that the maximum-power current is estimated with very high reliability, with $R^2$ values close to unity in almost all cases. Voltage estimation is less stable and depends more strongly on technology and temperature sensor location. The reconstructed I-V curves are physically admissible for most crystalline silicon, HIT, and CdTe modules, whereas CIGS and amorphous silicon modules exhibit lower admissibility. The proposed method should therefore be understood as an environmental-data-driven reconstruction tool when complete I-V curves are unavailable, rather than as a replacement for direct full-curve fitting techniques such as TSLLS or Reduced Form.