Concerns about climate change, pollution and energy security have prompted policies aiming at replacing fossil fuels (in heating and cooling, and transportation) with electricity, presumably generated from renewable sources. Climate change itself is expected to increase the demand for cooling in buildings, which is generally met with electricity-powered air conditioning. We use hourly electricity demand from a sample of Italian residences over a full year to examine how sensitive residential demand is to temperature. Our regression model includes a rich set of household-by-time fixed effects to control for dwelling characteristics and equipment, family composition, work and business schedules, demand for lighting, and seasonal habits other than temperature. These allows us to separate the effect of temperature from the demand for lighting and from other seasonal effects that may be correlated with temperature, but are not temperature. We find that demand stays unchanged within a relatively narrow range (and is thus relatively flat) up to temperatures of about 24.4 °C, and increases sharply with temperature thereafter. We find that temperature accounts for a very small share of daily electricity demand. Only on exceptionally hot summer days can temperature account for 12% of hourly electricity use.