Sub-Saharan Africa faces severe overheating problems during hot periods due to substandardly constructed buildings and high-priced energy services. Global warming is expected to aggravate the situation. Although literature addresses the effects of climate change on buildings in different world regions, how it will impact the Sub-Saharan region is still being determined, particularly in terms of design parameters and how they will vary. This study assesses the influence of design parameters on the cooling energy demand of a small-scale office building in Lagos and Kano, Nigeria. A Morris sensitivity analysis was carried out to rank and compare the influence of different design parameters on energy consumption, determined using EnergyPlus for present-day typical weather and the SSP5-8.5 scenario. The future scenario was generated using the Future Weather Generator, a morphing tool. The results show that, in 2080, the cooling load will increase from 1551 kWh/a to 2612 kWh/a (68.4 %) in Kano and from 1931 kWh/a to 3093 kWh/a (60.1 %) in Lagos. The cooling load in Lagos will generally be higher than in Kano by 18.4 % (596 kWh/a). The results indicate that reductions in the thermal conductivity of the east wall and decreases in the solar absorptance of the east wall, roof, and west wall elements will be the most significant factors affecting cooling in Kano. In Lagos, reductions in the thermal conductivity of the east wall and decreases in solar absorptance of both the east wall and roof elements will be the most influential.