The potential for critical infrastructure failures during extreme weather events is rising. Major electrical grid failure or "blackout" events in the United States, those with a duration of at least 1 h and impacting 50,000 or more utility customers, increased by more than 60% over the most recent 5 year reporting period. When such blackout events coincide in time with heat wave conditions, population exposures to extreme heat both outside and within buildings can reach dangerously high levels as mechanical air conditioning systems become inoperable. Here, we combine the Weather Research and Forecasting regional climate model with an advanced building energy model to simulate building-interior temperatures in response to concurrent heat wave and blackout conditions for more than 2.8 million residents across Atlanta, Georgia; Detroit, Michigan; and Phoenix, Arizona. Study results find simulated compound heat wave and grid failure events of recent intensity and duration to expose between 68 and 100% of the urban population to an elevated risk of heat exhaustion and/or heat stroke.