To investigate the link between rising global temperature and global energy use, we estimate an energy demand model that is driven by temperature changes, prices and income. The estimation is based on an unbalanced panel of 157 countries over three decades. We limit the analysis to the residential sector and distinguish four different fuel types (oil, natural gas, coal and electricity). Compared to previous papers, we have a better geographical coverage and consider non-linearities in the impact of temperature on energy demand as well as temperature-income interactions. We find that oil, gas and electricity use are driven by a non-linear heating effect: Energy use not only decreases with rising temperatures due to a reduced demand for energy for heating purposes, but the speed of that decrease declines with rising temperature levels. Furthermore we find evidence that the temperature elasticity of energy use is affected by the level of temperature as well as the level of income.