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The paper examines the theoretical issues of using borehole temperature survey data to control a frozen wall formed around the sinking mine shafts of the Nezhinsk mining and processing plant potash mine. We consider adjusting the parameters of the mathematical model of the frozen soil based on temperature measurements in boreholes. Adjustment of the parameters of the mathematical model (thermophysical properties of the soil) is usually carried out by minimizing the discrepancy functional between the experimentally measured and model temperatures in the temperature control boreholes. An important question about the form of this functional and the existence of minima remained after the previous studies. The study aimed at this question included analysis of heat transfer in two horizontal layers (sand and chalk) for two shafts under construction using artificial ground freezing. It was shown that the discrepancy functional minimum under certain conditions moves over time or is nonunique. This phenomenon results in ambiguity in adjusting the mathematical model parameters in the frozen soil to fit the borehole temperature survey data. At the stage of the frozen wall growth, the effective thermal conductivity in the frozen zone can be determined ambiguously from the temperature measurements in the boreholes—its value can change over time. At the stage of maintaining the frozen wall, the solution turns out to be dependent on the ratio of effective thermal conductivities in the frozen and unfrozen zones.