Flexible photovoltaic roofs (FPR) are suitable for curved and lightweight buildings due to lightweight, bendable, and easy-to-install characteristics, making them a promising direction for building-integrated photovoltaics (BIPV) in urban renewal. However, the limited heat dissipation capacity of FPR leads to elevated module temperatures, which reduces photovoltaic conversion efficiency and power generation, hindering its engineering application. Based on passive thermal management using phase change material (PCM), this study proposes a theoretical calculation model modified by the enthalpy method for thermal balance. Using meteorological data from cities across China’s five climatic zones (from severe cold to hot summer and warm winter), the effects of phase change temperature (25–45 °C) and thickness (20–60 mm) on temperature regulation and power performance of the FPR-PCM system are investigated. Results show that the effect of latent and sensible heat of PCM significantly suppresses temperature rise in PV modules, with a maximum temperature reduction of 35.46% and a maximum power increase of 16.24% during summer in Guangzhou. Climate adaptability analysis indicates stable annual regulation performance in low-latitude regions such as Guangzhou (monthly increase at ~2 kW·h), while significant seasonal variations are observed in high-latitude regions such as Harbin. Further considering building load and economic constraints, optimized thresholds for PCM layer thickness (≤60 mm) and recommended temperatures (35–45 °C for high-temperature regions; 25–30 °C for temperate regions) are proposed. This study can provide theoretical and technical references for climate-adaptive design of BIPV systems.