In many US cities, indoor exposure to heat continues to be the underlying cause of a considerable fraction (up to 80% during extreme events) of heat-related mortality and morbidity, even in locations where most citizens have air conditioning (AC). Nevertheless, the existing literature on indoor exposure to heat often regards AC as a binary variable and assumes that its presence inevitably results in a safe thermal environment. This is also reflected in heat vulnerability assessments that assign a binary attribute to AC. In this study, we used thermal simulation of buildings to investigate overheating in residential buildings in three US cities (Houston, Phoenix, and Los Angeles) and focused on scenarios where an AC system is present; yet not fully functional. Moreover, we identified the role of key building characteristics and investigated the sensitivity of indoor environment to the ambient temperature. Our results show that energy poverty and/or faulty systems can expose a considerable fraction of AC-owning elderly in Phoenix and Houston to excess heat for more than 50% of summer. This highlights the need to reevaluate AC as the primary protective factor against heat and introduces several implications that need to be considered in heat vulnerability assessments.