One of the grimmer terms I have come across in epidemiology is 'forward harvesting' - referring to the possibility that events like heatwaves may cause a high mortality rate but only by bringing forward the deaths of those who would have died in the short term anyway.
Although this seems likely, given that events like heatwaves and cold spells primarily affect the elderly there does not not seem to be much evidence for it. In fact there seems to be no evidence for it in cold spells and only a weak effect in some studies on hot spells. Because we have large data sets the effect, if there is one, cannot be large.
eg for the 2003 heatwave in Europe and especially France:
Impact of the 2003 Heatwave on All-Cause Mortality in 9 French Cities
There was no evidence to suggest that the extras deaths associated with the heatwave were simply brought forward in time.
and for a series of heatwaves and cold spells in Holland:
The Impact of Heat Waves and Cold Spells on Mortality Rates in the Dutch Population
The results concerning the forward displacement of deaths due to heat waves were not conclusive. However, looking at the relation between the ambient temperature and mortality over the whole period studied, our results showed compensatory effects on mortality in the longer lag periods after warm weather (average temperature above optimum temperature level). This could be an indication of a harvesting effect of warmer temperatures. However, as previously discussed, this was not clearly shown by the analysis of heat waves. We found no cold-induced forward displacement of deaths.