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The temperature-mortality relationship follows a well-known J-V shaped pattern with mortality excesses recorded at cold and hot temperatures, and minimum at some optimal value, referred as Minimum Mortality Temperature (MMT). As the MMT, which is used to measure the population heat-tolerance, is higher for people living in warmer places, it has been argued that populations will adapt to temperature changes. We tested this notion by taking advantage of a huge migratory flow that occurred in Italy during the 1950s, when a large number of unemployed people moved from the southern to the industrializing north-western regions. We have analyzed mortality-temperature relationships in Milan residents, split by groups identified by area of birth. In order to obtain estimates of the temperature-related risks, log-linear models have been used to fit daily death count data as a function of different explanatory variables. Results suggest that mortality risks differ by birthplace, regardless of the place of residence, namely heat tolerance in adult life could be modulated by outdoor temperature experienced early in life. This indicates that no complete adaptation might occur with rising external environmental temperatures.