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This paper presents an approach of empirical modeling of the machining process physical quantity with measurement uncertainty parameter included in the resulting power mathematical model coefficients. The proposed approach is presented through an example of modeling of the average temperature in turning like a methodology that is under the influence of various sources of measurement errors. The uncertainty budget accounts for the sources of errors of the experimental measuring system and the cutting process itself. This approach enables estimation of the reliability of the gained mathematical models and gives the possibility of identification and lowering of the main sources of errors.