This paper is from 2007, Extreme Weather Events, Mortality and Migration by Olivier Deschenes and Enrico Moretti. From the abstract:
We estimate the effect of extreme weather on life expectancy in the US. Using high frequency mortality data, we find that both extreme heat and extreme cold result in immediate increases in mortality. However, the increase in mortality following extreme heat appears entirely driven by temporal displacement, while the increase in mortality following extreme cold is long lasting. The aggregate effect of cold on mortality is quantitatively large. We estimate that the number of annual deaths attributable to cold temperature is 27,940 or 1.3% of total deaths in the US. This effect is even larger in low income areas. Because the U.S. population has been moving from cold Northeastern states to the warmer Southwestern states, our findings have implications for understanding the causes of long-term increases in life expectancy. We calculate that every year, 5,400 deaths are delayed by changes in exposure to cold temperature induced by mobility. These longevity gains associated with long term trends in geographical mobility account for 8%-15% of the total gains in life expectancy experienced by the US population over the past 30 years. Thus mobility is an important but previously overlooked determinant of increased longevity in the United States. We also find that the probability of moving to a state that has fewer days of extreme cold is higher for the age groups that are predicted to benefit more in terms of lower mortality compared to the age groups that are predicted to benefit less.Within the paper, they observe that heat spikes lead to a rise in mortality rates which then fall immediately afterwards while speaks in extreme cold also generate higher mortality rates but rates which do not decline as quickly once the aberrant temperature has passed.
The broader point is that to live longer lives, Go South.