Concurrent with a rapid rise in temperatures within US cities, the frequency of regional electric grid system failures is also rising in recent decades, resulting in a growing number of blackouts during periods of extreme heat. As mechanical air conditioning is a primary adaptive technology for managing rising temperatures in cities, we examine in this paper the impact of a prolonged blackout on heat exposure in residential structures during heat wave conditions, when air conditioning is most critical to human health. Our approach combines a regional climate modeling system with a building energy model to simulate how a concurrent heat wave and grid failure event impacts residential building-interior temperatures across Phoenix. Our results find a substantial increase in heat exposure across residential buildings in response to the loss of electrical power and mechanical cooling systems, with such an event potentially exposing more than one million residents to hazardous levels of heat. We further find the installation of cool roofing to measurably lower the risk of extreme heat exposure for residents of single-story structures.