Like SC (comment further below), I too have trouble with using annual average temperatures to talk about heat waves, though I've used them myself for other purposes. It's the extremes of heat (and cold) that kill people. Most of the deaths are among the ill and the elderly, just as it would be in nature.

For species less adaptible than ours, the extremes in temperature (and precipitation) are much more important than the annual averages in affecting the health and reproduction of natural populations. Plants and animals are affected, like us, by drought, blizzards, heat waves, etc. The effects tend to be most pronounced towards the edges of their geographic distributions.

I haven't run across a summary measure for heat waves, which is not to say there isn't one. However, I have looked at the annual highest temperature for 36 representative climate monitoring stations in British Columbia, where I live, for the period 1950-2001. Only about a third of the locations show evidence for any increase in the maximum temperature. The increase at those locations is about a degree Celsius in 50 years.

Reasonably complete data sets are pretty rare in my experience, especially when looking at locations with records back into the 19th century. The outcome of even simple analyses can be affected by how the missing data are treated. Temperature records have been kept in BC for about 150 years, but the analysis back to 1950 is probably the best that can be done with confidence.