In the tasks of predicting the volumes of methane emissions from thermokarst lakes in the Arctic territories, as one of the causes of modern global warming, it is necessary to use, along with climatic characteristics, data on the dynamics of lake areas, which are usually obtained using satellite imagery. Due to the large number of cloudy days in the northern territories, it is possible to obtain only a small number of cloudless images, which leads to significant omissions in the time series of lake areas. To restore the missing values of the area of the lakes, it is proposed to use a new approach to the restoration of missing values based on the methods and algorithms of entropy-randomized machine learning. The work is supposed to restore the missing values in the experimental data on the areas of thermokarst lakes using time series of average annual temperature and annual precipitation. As experimental data on the thermokarst lakes areas and climatic parameters (temperature and amount of precipitation), we used the results of studies conducted in the Arctic zone of Western Siberia from 1973 to 2007. Studies were conducted in nine test sites selected in different permafrost zones (continuous, discontinuous and insular). Data on the average annual temperature and annual precipitation for each test site were obtained by reanalysis. The developed algorithm for recovering missing values within the framework of this approach is implemented using the MATLAB R2019a tools. The missing values are calculated for the selected nine test sites. To illustrate, the time series of the values of the area of lakes, temperature and precipitation in one of the test sites are shown. An analysis of the omissions recovery errors was carried out, which showed that the developed algorithm allows us to restore the missing values of the lake areas from the data on changes in temperature and precipitation with practically acceptable accuracy.