Heat waves are considered one of the most noteworthy extreme events all over the world due to their crucial impacts on both society and the environment. For the present article, a relatively new heat wave index, which was primarily introduced for the study of extreme warming conditions over Australia (Excess Heat Factor (EHF, hereafter)), was applied over Greece (eastern Mediterranean) for a 55-year period in order to examine its applicability to a region with different climatic characteristics (compared to Australia) and its ability to define previous exceptional heat waves. The computation of the EHF index for the period 1958–2012 demonstrated that, during the warm period of the year (June, July, August, and September (JJAS)), Greece experiences approximately 20 days per year with positive anomalous conditions (EHF > 0) with positive statistically significant trends for all stations under study. Moreover, an average of 128 spells with a duration of 3 to 10 consecutive days with positive EHF values were found during the examined 55-year period. As the duration of the spell was extended, their frequency lessened. Finally, it was found that the EHF index not only detected, identified, and described efficiently the characteristics of the heat waves, but it also provided additional useful information regarding the impact of these abnormal warming conditions on the human ability to adapt to them.