I recommend to also consider report to the EU published in 2007. It looked at the 15,000 additional deaths in France caused by the heat wave in August 2003. It also looked at the excess mortality in 12 European countries during the summer 2003:
In total, more than 80,000 additional deaths were recorded in 2003 in the twelve countries concerned by excess mortality compared to the 1998‐2002 period. Whereas 70,000 of these additional deaths occurred during the summer, still over 7,000 occurred afterwards. Nearly 45,000 additional deaths were recorded in August alone, as well as more than 11,000 in June, more than 10,000 in July and nearly 5,000 in September. The mortality crisis of early August extended over the two weeks between August 3rd and 16th. 15,000 additional deaths were recorded in the first week and nearly 24,000 in the second. The excess mortality in this second week reached the exceptional value of 96.5% in France and over 40% in Portugal, Italy, Spain and Luxembourg. Excess mortality exceeded 20% in Germany, Switzerland and Belgium and 10% in all the other countries.
I am sure that whether this demonstrated increase in mortality due to an heat wave will be partly compensated by a putative decline in mortality in colder regions does not make any difference to the families of the 80,000 people who passed away in just 4 months.
Robine J.-M., Cheung S. L., Le Roy S., Van Oyen H. & Herrmann F. R., 2007. Report on excess mortality in Europe during summer 2003. EU community Action Programme for Public Health, Grant Agreement 2005114. Heath Wave Project 2003. http://ec.europa.eu/health/ph_projects/2005/action1/docs/action1_2005_a2_15_en.pdf