The aim of this paper is to develop a method of determining the heat transfer coefficients on the inner surface of the pipeline and outer surface of the thermometer used to measure the temperature of a fluid flowing under high pressure. The method is based on the solutions to the inverse heat conduction problems for the thermometer and the pipeline wall. The heat transfer coefficients are determined based on the measurement of the temperature of a cylindrical metal thermometer and the temperature of the wall of a cylindrical pipeline. The temperature sensor is located in the pipeline wall close to the inner surface. The correlations for the Nusselt numbers used to determine heat transfer coefficients on the outer surface of the thermometer and the inner surface of the pipeline contain unknown coefficients which are found using the least squares method. The unknown coefficients are selected so that the sum of the squares of differences between the fluid temperature determined based on the measurement of the temperature of the pipeline wall and the fluid temperature obtained from measurements inside the thermometer, calculated for several dozen set time points, is as small as possible.