AlSb and AlAs have attracted renewed interest in recent years as promising photovoltaic (PV) materials due to significant light absorption, eco-friendliness, and low cost. Here, density functional theory (DFT) in combination with the non-equilibrium Green's function method (NEGF) has been used to compute the temperature-dependent PV parameters of nanoscale AlSb and AlAs p-n junction solar cell devices. In particular, the influence of electron-phonon coupling (EPC) and spin-orbit coupling (SOC) on the PV properties of these devices is investigated. Our results highlight the importance of inclusion of EPC in evaluating the ab initio PV properties of p-n junctions at finite temperatures. At non-zero temperatures, the PV parameters can differ significantly compared to those at zero temperature due to phonon-assisted tunnelling of charge carriers across the p-n junction. In particular, the mobility of low-effective-mass carriers at the p-n junction is found to be enhanced by phonon scattering, which in turn results in improved PV transport properties. The short-circuit current (Jsc) at 300 K proved to be 21.7% (16.2%) higher for AlSb (AlAs) than that at 0 K. On the other hand, the open-circuit voltage (Voc) at 300 K proved to be 19.1% (16.7%) lower for AlSb (AlAs) than that at 0 K. Jsc is higher in AlSb than in AlAs due to higher phonon-influenced mobility of low-effective-mass carriers. Overall, our study strongly suggests the importance of inclusion of EPC and hence phonon scattering in the first-principles quantitative determination of PV parameters of solar cells. The estimates obtained in this study may be utilized as input ab initio parameters in continuum-model-based multi-scale simulations of AlSb and AlAs p-n homo-junction solar cells.