This study investigated the thermal fatigue reliability of ball grid array (BGA) solder joints under accelerated thermal cycling, considering the impacts of solder alloy and temperature profile. Applying the Darveaux solder joint reliability assessment, simulations consider lead-based (63Sn37Pb and 62Sn36Pb2Ag) and lead-free (SAC105, SAC305, and SAC405) solder alloys under temperature profiles: 0°C (Tmin) to 100°C (Tmax), −40°C to 85 °C, −40 °C to 125 °C, and −40 °C to 150 °C. Results indicate that SAC305 exhibited the highest equivalent stress, while 63Sn37Pb demonstrated the highest plastic strain and creep strain energy density. SAC105 displayed the lowest stress and strain parameters. Moreover, increasing the thermal cycling temperature range intensifies stress, strain, and damage parameters, with −40 °C to 150 °C showing the highest magnitudes. SAC405 exhibited superior thermal fatigue life compared to other alloys, with its cycles to failure outperforming 63Sn37Pb, SAC105, 63Sn36Pb2Ag, and SAC305 by 16832, 11992, 6218, and 3601 cycles, respectively. Lower temperature ranges enhance thermal fatigue life, with 0 °C to 100 °C recording 8%, 33%, and 53% higher life than −40 °C to 85 °C, −40 °C to 125 °C, and −40 °C to 150 °C, respectively. Notably, higher silver content and lower temperature ranges were associated with increased thermal fatigue life, providing valuable insights for BGA solder joint reliability enhancement.