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&amp;nbsp; This article is devoted to the mathematical modeling and computing experiment in problems of temperature fields forecast in continuous foundations in cryolithozone, which will provide a qualitative approach to non-stationary thermal calculations for making design decisions to ensure the stability and reliability of bases and foundations of buildings in the Arctic zone.&amp;nbsp; The article formulates the problem of forecasting by determining changes in the temperature, areal distribution, thickness, and vertical structure of permafrost, seasonal and perennial freezing of the soil, their temperature strength state, and properties in connection with the construction of buildings. Presented mathematical calculations are based mainly on the assumption of a non-stationary process of heat exchange. Mathematical models for determining depth of thawing are considered. The problem of determining the temperature in the basement of the foundation, limited on the one side, in which the temperature depends on only one coordinate with the condition that the surface temperature of the permafrost soil undergoes periodic fluctuations around zero value under the influence of external influences, has been solved. It is demonstrated that the two-dimensional problem of permafrost ground with a semi-infinite foundation thickness can be generalized even more. The problem is formulated in the form of a differential equation of heat balance taking into account the heat flux, which varies according to the Fourier&amp;rsquo;s law. &amp;nbsp;	

Calculation methods of non-stationary temperature fields influence on foundation in cryolithozone