We compare heat-related mortality impacts for three European cities, London, Lisbon and Budapest, under five climate change policies representing different dates at which carbon dioxide (CO2) emissions peak, rates at which emissions decline, and emissions floors, and compare them with a non-mitigation business-as-usual emissions scenario, for three time periods, the 2030s, 2050s and 2080s. Under an SRES A1B business-as-usual emissions scenario and using climate projections from 21 GCMs, heat-related mortality rates (per 100,000 of the population) attributable to climate change in the 2080s are simulated to be in the range 2-6 for London, 4-50 for Lisbon and 10-24 for Budapest. Whilst the policy scenarios serve to reduce the number of heat-related deaths attributable to climate change, by up to 70% of the A1B impacts under an aggressive mitigation scenario that gives a 50% chance of avoiding a 2 ¡C global-mean temperature rise from pre-industrial times, they do not eradicate the effects of climate change on heat-related mortality. The magnitude of avoided impacts is minor in the early 21st century but increases towards the end of the century. Importantly, the magnitude of avoided impacts is more sensitive to the year at which emissions are reduced than to the rate at which emissions are reduced.