This paper describes a mathematical method for estimating static formation temperatures using a function based on extrapolation of the measured data in the thermal recovery process of geothermal and petroleum wells. This method uses the least squares fit of a rational polynomial model to describe the transient temperature data and also provides an analytical expression of thermal recovery processes. This expression gives the asymptotic value for final temperature. We then apply this method for estimating static formation temperatures of a geothermal and petroleum drilled well. In this work we have developed the equations of least squares fit of rational polynomial function and used the equation to estimate the uncertainties of its coefficients. This fitting procedure allows us to obtain a mathematical model that represents the thermal recovery process and to extrapolate the value of final temperature. This is a practical method to estimate static formation temperature, having the advantages that the thermal properties of the drilling mud and its formation are not required; it can also be used in the geothermal and petroleum industries. (C) 2015 Elsevier Ltd. All rights reserved.