Climate change is one of the greatest challenges facing the building sector and rural areas in particular should be prioritised due to their special characteristics. In this work, ways to adapt rural residential buildings in a Mediterranean climate to climate change via energy renovation were studied, taking La Rioja (Spain) as a case study. Different energy renovation solutions were evaluated under different climate change scenarios considering the possible evolution of the climate zones. The energy and economic impacts of these energy-renovated buildings were compared to those of existing buildings. Nearly zero-energy buildings were achieved by changing the thermal envelopes and their corresponding interior partitions. The study discovered that, on the one hand, the heating energy demand was reduced while the cooling energy demand was increased, thus reducing the total energy demand; on the other hand, the best energy renovation solution entails compliance by nearly zero-energy buildings with current building thermal regulation for the current climate zone. This work can serve as a guide to establish and promote energy renovation policies that are effective in addressing climate change and are economically viable. Furthermore, the methodology developed and the results obtained can be extrapolated to other cold Mediterranean climate zones.