Global warming is expected to lower the energy demand for heating, which would contribute to a decline in CO2 emissions. This effect may be offset by energy needs for additional cooling and by the impacts of households that reinvest the money they save on heating partly for greater thermal comfort but also for the consumption of other goods and services (rebound effects). These effects would be particularly significant in a country such as Switzerland, for which heating accounts for a large share of its CO2 emissions (28%) and which imports all its fossil fuels. This paper analyzes the impacts of global warming on the Swiss energy demand for space heating and cooling over the period 2010-2060. Climate projections are used to compute the changes in heating (HDD) and cooling degree-days (CDD), which determine the demand for space conditioning. We use the computable general equilibrium (CGE) model GEMINI-E3 to take into account the many interactions between supply and demand and to assess the general equilibrium effects of climate change on energy use. Several scenarios are simulated to analyze the impacts on energy used for space conditioning by households and the services and industry sectors. We also perform a sensitivity analysis on key variables related to the climate change scenarios and the penetration of air-conditioning systems. We find significant and positive welfare effects from reduced heating needs. This effect largely outweighs the increased electricity used for cooling.