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Abstract. Measurement temperatures by (some devises) are applied immediately after shut-down and may be corrected for the temperature drop that occurs in the interval between shut-down and measurement. This paper presents a new procedure for thermal modelling of the tool cutting used just after machining; when the tool is out off the chip in order to extrapolate the cutting temperature from the temperature measured when the tool is at stand still. A fin approximation is made in enhancing heat loss (by conduction and convection) to air stream is used. In the modelling we introduce an equivalent thermal network to estimate the cutting temperature as a function of specific energy. In another hand, a local modified element lumped conduction equation is used to predict the temperature gradient with time when the tool is being cooled, with initial and boundary conditions. These predictions provide a detailed view of the global heat transfer coefficient as a function of cutting speed because the heat loss for the tool in air stream is an order of magnitude larger than in normal environment. Finally we deduct the cutting temperature by inverse method. Key words: cutting tool cooling, equivalent thermal resistance, inverse method, milling, cutting temperature