Most residential buildings and capital structures in the permafrost zone are constructed on the principle of maintaining the frozen state of the foundation soils. The changing climate and the increasing anthropogenic impact on the environment lead to changes in the boundaries of permafrost. These changes are especially relevant in the areas of piling foundations of residential buildings and other engineering structures located in the northern regions since they can lead to serious accidents caused by the degradation of permafrost and decrease the bearing capacity of the soil in such areas. Therefore, organization of temperature monitoring and forecasting of temperature changes in the soil under the buildings is an actual problem. To solve this problem, we use computer simulation methods of three-dimensional nonstationary thermal fields in the soil in combination with real-time monitoring of the temperature of the soil in thermometric wells. The developed approach is verified by using the temperature monitoring data for a specific residential building in the city of Salekhard. Comparison of the results of numerical calculations with experimental data showed good agreement. Using the developed computer software, nonstationary temperature fields under this building are obtained and, on this basis, the bearing capacities of all piles are calculated and a forecast of their changes in the future is given. To avoid decreasing the bearing capacity of piles it is necessary to prevent the degradation of permafrost and to supply the thermal stabilization of the soil. The proposed approach, based on a combination of the soil temperature monitoring and computer modeling methods, can be used to improve geotechnical monitoring methods.