When heat waves coincide with loss of access to air conditioning (e.g., due to power outages), the adverse impacts on well-being of occupants will be exacerbated. Hence, there is ongoing interest in using passive strategies to improve the resiliency of buildings under such conditions. One promising strategy is the use of conventional or latent thermal mass to passively mitigate overheating. As a result, Phase Change Materials (PCM), which are already promoted widely as a strategy to use solar energy for passive heating in buildings, may also be a useful strategy to avoid summertime overheating. To verify this, we used whole-building energy simulations to study the effectiveness of PCMs in improving the resiliency of buildings during extreme events. The results suggest a considerable dependence on the timing and duration of power/air conditioning loss episode, the melt temperature of the material, and the underlying climate. We used parametric runs to study the effect of melt temperature on PCM effectiveness to reduce energy consumption while simultaneously increasing the resiliency of buildings during power outages. The results suggest that under some conditions it is possible to optimize melt temperature for both energy efficiency and heat resiliency, while under other conditions, optimizing for one outcome adversely affects the other.