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• The potential of energy saving by using adaptive setpoint temperatures. • The influence of thermostats according to their accuracy: 0.1, 0.5, and 1 °C. • The analysis of two case studies in the current scenarios, 2050 and 2100. • The 0.5 and 1 °C thermostats achieved energy savings of more than 40%. Building energy performance should be improved to reduce the impact of climate change. The energy saving potential has been recently proved with adaptive setpoint temperatures. However, the accuracy of thermostats hinders the achievement of the energy saving obtained in previous studies. For this reason, this paper studies the influence of three types of thermostats according to their configuration accuracy: 0.1, 0.5, and 1 °C. Two case studies (with and without retrofitting) were analysed in three cities in the current scenario, in 2050, and in 2100. The results showed that the implementation of adaptive setpoint temperatures in thermostats of 0.1 °C virtually obtains the same savings as the direct application of thermal comfort limits. Nevertheless, obtaining considerable energy savings in the other two thermostats depends on the type of energy consumption, climate, and the category of the thermal comfort model. The application of adaptive setpoint temperatures in air conditioning systems obtains energy savings greater than 40%, regardless of the type of thermostat and category, whereas in heating systems, only the category III obtains energy savings with old thermostats. [ABSTRACT FROM AUTHOR]