Energy consumption of buildings for cooling purposes partially depends on outdoor ambient air temperatures. Measured data from eight Hellenic islands in the Ionian and the Aegean sea is used to estimate the frequency of high temperature exceedance in these islands, useful for estimates of building cooling demand and comfort conditions in the area. The analysis is based on the calculation of the daily T-E value, which is the sum of the daily minimum outdoor temperature and half of the daily temperature amplitude. This parameter corresponds to a daily average value of 9-10 h, during the period of May through September, when the hourly ambient temperature exceeds 26 and/or 28 degrees C in the regions of interest. The analysis carried out shows that a two-parameter exponential law, is in excellent agreement with the large values distribution for the parameter T-E.