Recently, due to the increase in the number and severity of heat waves, there is a growing interest in understanding overheating inside buildings and the associated health risks. As a result, a new area of research inquiry is emerging, focusing on investigating the possible trade-offs and synergies between energy efficiency strategies and resiliency to heat in residential buildings. This study addresses this challenge using whole-building simulations to model the passive survivability of archetype residential buildings during power failure scenarios that coincide with extreme heat conditions in Houston, TX and Phoenix, AZ. Results suggest that in older constructions, the indoor thermal conditions will easily reach dangerous levels during such episodes. In both cities, the discomfort index reaches the critical threshold in less than 6 h after the power outage. In addition, while there is a notable overlap between the two objectives, the implication of energy efficiency strategies on building resiliency to heat depends strongly on building characteristics and underlying climate. Notably, in contrast to previous studies that consider colder climates, increasing the insulation and air-tightness are found to be beneficial to passive survivability. Finally, our analysis highlights the importance of the definition of thermal resiliency metrics in interpreting the results of the simulations.