The inherent power fluctuations of wind, photovoltaic (PV) and bioenergy with carbon capture and storage (BECCS) create a temporal mismatch between energy supply and demand. This mismatch could lead to a potential resurgence of fossil fuels, offsetting the effects of decarbonization and affecting the realization of the Paris target by limiting global warming to below 2 °C in the 21st century. While application of energy storage is widely recommended to address this limitation, there is a research gap to quantify the impacts of energy storage limitation on global warming. Here, we analyzed the hourly variation of global wind and PV power during the period 1981–2020 and the monthly capacity of biomass production in 2019, and thus quantified the impact of decreasing the capacity of energy storage on global warming using a state-of-the-art Earth system model. We found that global warming by 2100 in the SSP1-2.6 scenario would increase by about 20% and exceed 2 °C without deploying energy storage facilities. Achieving the 2 °C target requires reducing power losses of wind and PV by at least 30% through energy storage. This requirement delivers to a cumulative storage capacity of 16.46 TWh using batteries during the period 2021–2100, leading to the international trade of cobalt and manganese across countries due to deficits of minerals at a country level. In the context of energy security, we highlight the importance of considering the limitations of energy storage and mineral shortage in the forthcoming policies of decarbonization.