Heat waves and other extreme weather events have attracted a great deal of attention due to their socioeconomic impacts and relation to climate change. A heat wave is defined through a general loss function that captures its amplitude, temporal persistence, and spatial extent. The proposed statistical framework is at the nexus of extreme value theory (EVT) and functional data analysis (FDA) and enables computation of probabilities of yet unobserved rare events that are not seen in historical records. Data from the North American Regional Climate Change Assessment Program, which has produced computer model predictions of current and future temperatures across much of North America, are used. The approach allows for the computation of probabilities for heat waves of any pre-specified temporal duration, spatial extent, and overall magnitude. It can be applied to the computation of probabilities of other extreme weather events, including cold spells and droughts.