Abstract <p>The problem considered in the paper is evaluation of future changes in the characteristics of rare annual maximum air temperatures on the territory of Russia. An analysis of changes in climate extreme indices is based on the results of a great ensemble of simulations performed using a high-resolution regional climate modeling system under the SSP5-8.5 anthropogenic impact scenario. The study focuses on characteristics of rare air temperature extremes with a specified period of averaging, which are determined using a nonstationary approach to probabilistic analysis of extreme values. Particular attention is paid to the uncertainty of evaluation during different time intervals in the 21st century. Important regional differences have been revealed in the sensitivity of the indices to future climate changes. The results of the study can be used as a base for assessing risks of critical impacts and optimizing climate-driven decisions.</p>