Heat waves can have devastating impacts on society, but a current weakness with the analysis and modeling of heat waves is the negligible use of the Statistical Theory of Extreme Values (EVT). This is a branch of statistics more appropriate for studying extreme events such as heat waves, floods, etc. For this study, EVT was used to develop methods for analyzing heat waves and their characteristics (frequency, intensity, duration, etc.). This analysis was performed using temperature data from Phoenix, AZ and Fort Collins, CO. This study signaled how Statistical Theory of Extreme Values can be applied to model certain features of heat waves. Results from the analysis showed an increase in the summer highest temperature and in the number of heat waves per year for both cities. This study also explored other characteristics of heat waves (heat wave duration and individual maximum temperatures within heat waves), indicating how the extreme value approach would need to be extended to fully model all features of heat waves. The results show there hasn't been a significant change in the intensity or duration of heat waves for either city. The results as well descriptively imply a temperature dependence of daily temperatures within a heat wave for both cities. More reliable quantification of return levels for severe heat waves, including any trends in their characteristics, and other extreme events involving spells will be achieved with the continual development and future use of these methods.