The most important data on the thermal regime of the Earth's interior come from temperature measurements in deep boreholes. The drilling process greatly alters the temperature field of formations surrounding the wellbore. In permafrost regions, due to thawing of the formation surrounding the wellbore during drilling, representative data can be obtained only by repeated observations over a long period of time (up to 10 years). Usually a number of temperature logs (3-10) are taken after the well's shut-in. Significant expenses are required to monitor the temperature regime of deep wells. In this paper, we introduce a new approach in predicting the undisturbed formations temperatures from shut-in temperature logs in deep wells. The main features of the suggested method are following: the refreezing of the thawed formations (around the wellbore) is completed, the temperature logs are taken after refreezing, the starting point in the well thermal recovery is moved from the end of well completion to the moment of time when the first shut-in temperature log was conducted. It is shown that after refreezing the further cooling of a well can be approximated by a constant (per unit of length) linear heat source. Hence, the Horner equation can be used for predicting the temperature of frozen formations for estimation of the formation temperature. A simple method to process field temperature data is presented. To demonstrate this approach, temperature shut-in time data for four depths from four wells in Alaska were successfully used.