A model of propagation of thermal fields in permafrost from various engineering objects operating in Arctic regions is considered. The proposed model includes the most significant technical and climatic parameters affecting the formation of thermal fields in the surface layer of the soil. The main objective of the study is a long-term forecasting of changes in the dynamics of permafrost boundaries during operation of cluster sites of northern oil and gas fields. Such a forecast is obtained by simulation of complex system consisting of heat or cold sources and frozen soil, thawing of which can lead to the loss of the bearing capacity and possible technogenic and environmental accidents. For example, the sources of heat can be production wells, and the sources of cold can be seasonal cooling devices that are used to stabilize the soil. To minimize the impact of heat sources on permafrost, various options for thermal insulation are used, and to preserve the original temperature regime of the top layer of soil, riprap materials consisting of sand, concrete, foam concrete, or other heat insulating material are used. The developed set of programs was used in the design of 12 northern oil and gas fields. To solve the described problem in a complex three-dimensional area, substantial computational resources are required. The computing time of one variant can often exceed 10-20 hours of machine time on a supercomputer. To speed up the numerical calculations, multi-core processors are used. Numerical calculations illustrate the possibility of a developed set of programs for making long-term forecasts for determining changes in the boundaries of the permafrost zones, and show that on multi-core processors it is possible to achieve acceleration close to the theoretical one.