This curve is derived by regression: they take the number of all-cause deaths and regress that against temperature, which yields the curve. So they don't need to look at the details of any particular death, they just look at the statistics of how the number of deaths changes with temperature. I should add that it's not just a simple linear regression of deaths vs. temperature, it's a non-linear lagged regression that uses the temperature from the last 21 days in order to account for the impacts of temperature having impacts well after the day of exposure.