The mechanical properties of high-temperature rocks, after being cooled by various methods, significantly influence the safety of deep earth geotechnical engineering. The study primarily investigated medium-weathered granite porphyry. Uniaxial compression and cyclic dynamic impact tests were performed on specimens cooled naturally and via water immersion at 400 ℃. The aim was to compare and analyze the change in the mechanical properties of granite. Utilizing the Logistic distribution law, loading damage variables and thermal cycling damage variables were incorporated to develop a statistical damage constitutive model for granite. The corresponding parameters were determined, and the applicability and reasonableness of the model were verified. The results reveal that during uniaxial compression testing, the internal microcracks in granite expand and coalesce into macroscopic cracks as the number of thermal cycles increases. Furthermore, the mass of the rock samples and longitudinal wave velocity decrease, while the elastic deformation phase in the static stress-strain curve shortens, indicating a distinct unstable damage stage. The rate of deterioration of rock strength can be significantly affected by the cooling method, but the final static compressive strength of granite is not significantly affected. Under an air pressure impact of 0.30 MPa, the dynamic compressive strength of naturally cooled granite initially increases and then decreases with increasing impact cycles. The initial impact enhances the compressive strength of naturally cooled granite. However, when thermal cycling exceeds three cycles, granite's resistance to cyclic impacts diminishes. The dynamic damage model, formulated using the Logistic distribution, exhibits good alignment with the experimental curve. The model parameters are readily obtainable, possessing a clear physical interpretation and practical applicability. This research offers valuable references for the construction, repair, and stability analysis of rock masses in variable temperature environments.