The regularities of the dynamics of the average annual temperature of Irkutsk from 1820 to 2019 were revealed. It is proposed to use the sum of temperatures. However, this indicator requires the continuity of the dynamic series, so for Irkutsk the sum of temperatures could be accepted only from 1873. The first three terms of the general wavelet model gave a very high correlation coefficient of 0.9996. The second indicator is a moving average, calculated as the ratio of the sum of temperatures to the current time. Here the first three wavelets gave a correlation coefficient of 0.9962. In the dynamics of the average annual temperature from 1820 to 2019, 86 wavelets were obtained, of which 47 affect the future. The temperature has a high quantum certainty, and the change in the average annual temperature of Irkutsk is obtained up to a measurement error of 0.05 °C, and the identification process occurs as a full wavelet analysis. The basis of the forecast in 200 years makes it possible to replace the non-linear two-term trend with an oscillatory perturbation. With an increase in the number of terms in the model, the ordinate of the average annual temperature increases: for three terms, the temperature interval is from –2.95 °C to 2.61 °C; for 12 members from –4.06 °C to 4.02 °C; for the forecast for 47 members for 2020- 2220, from –4.62 °C to 4.40 °C.