The present research aims to understand the cement hydration and microstructure formation mechanism of calcined phosphogypsum (CPG) supplemented calcium sulfoaluminate (CSA) pastes cured under hot-weather temperatures and to ensure the appropriate application and effective service of CSA cement-based materials, as well as to address the problem of overstocking of CPG. The effects of CPG dosage on the heat of hydration, electrical resistivity, hydration products, and bound water content of CSA cement pastes were investigated at curing temperatures of 20 °C, 35 °C, and 50 °C. Hydration kinetics was studied to elucidate the hydration mechanism, and thermodynamic modelling was performed to predict the phase assemblages. The results show that the incorporation of CPG facilitated the formation of ettringite and significantly reduced the transformation of ettringite to monosulfate, and these phenomena were enhanced with an increase in the CPG. The addition of CPG at elevated curing temperature (35 °C and 50 °C) significantly improved the compressive strength of CSA cement pastes. The growth rate and nucleation rate predicted by the BNG model for the CSA cement pastes cured at 50 °C were substantially higher compared to those at 20 °C.