Analytical dependences are given for determining the cutting temperature during grinding and turning based on the representation of the removed allowance in the form of a package of elementary straight-line adiabatic rods that are cut by a cutting tool during processing. Such an approach to calculating the cutting temperature makes it possible to evaluate technological capabilities of grinding and turning processes from a single point of view and scientifically substantiate the choice of the most effective method of finishing machining of machine parts. It is shown that during grinding the discrepancy between the calculated and experimental values of the cutting temperature is small - within 10%. When turning, this discrepancy increases to 2 times or more, which reduces the accuracy of the calculations. It is established that the reason for such a large discrepancy is the periodic (discrete) nature of the cutting by the cutting tool of elementary rectilinear adiabatic rods. Based on this, for a more accurate calculation of the cutting temperature during turning, the number of cuts of the adiabatic core, i.e. the number of elementary volumes of the processed material generated during the passage of the cutter cutting zone. The heat supply to the elementary rectilinear adiabatic rod was considered discretely varying in time. As a result of the calculations, it was found that in this case, the cutting temperature during turning decreases by about 2 times, and this brings the theory and practice of machining in line. It was also established that the smaller the number of elementary volumes of the processed material generated during the passage of the cutting zone by the cutter, the lower the cutting temperature. For example, when turning with the smallest possible number of elementary volumes of the processed material generated during the passage of the cutting zone by the cutter equal to 2, the cutting temperature can be reduced to 10 times.