A better quick test is all-cause mortality, which shows higher death rates in colder months. (https://www.cdc.gov/mmwr/volumes/68/wr/mm6826a5.htm) It's not ideal, because you'd need to measure the entire lifespan of people exposed to hpt climates, compared to those not.
I live in California's central valley, where typical heat waves are well over 100 °F, usually passing 110 °F a few times a year. The lifespan here isn't any shorter than in the colder counties, and the counties with the longest life expectency are pretty mixed between hot and cold. (https://fox5sandiego.com/news/health/counties-with-the-longe...)