The increase in the frequency and intensity of heat waves is one of the most unquestionable effects of climate change. Therefore, the progressive increase in maximum temperatures will have a clear incidence on the increase in mortality, especially in countries that are vulnerable due to geographical location or their socioeconomic characteristics. Different research studies show that the mortality attributable to heat is decreasing globally, and research is centred on future scenarios. One way of detecting the existence of a lesser impact of heat is through the increase in the so-called temperature of minimum mortality (TMM). The objective of this study is to determine the temporal evolution of TMM in two Spanish provinces (Seville and Madrid) during the 1983–2018 period and to evaluate whether the rate of adaptation to heat is appropriate. We used the gross rate of daily mortality due to natural causes (CIEX: A00-R99) and the maximum daily temperature (°C) to determine the quinquennial TMM using dispersion diagrams and realizing fit using quadratic and cubic curvilinear estimation. The same analysis was carried out at the annual level, by fitting an equation to the line of TMM for each province, whose slope, if significant (p < 0.05) represents the annual rate of variation in TMM. The results observed in this quinquennial analysis showed that the TMM is higher in Seville than in Madrid and that it is higher among men than women in the two provinces. Furthermore, there was an increase in TMM in all of the quinquennium and a clear decrease in the final period. At the annual level, the linear fit was significant for Madrid for the whole population and corresponds to an increase in the TMM of 0.58 °C per decade. For Seville the linear fits were significant and the slopes of the fitted lines was 1.1 °C/decade. Both Madrid and Seville are adapting to the increase in temperatures observed over the past 36 years, and women are the group that is more susceptible to heat, compared to men. The implementation of improvements and evaluation of prevention plans to address the impact of heat waves should continue in order to ensure adequate adaptation in the future.