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ver its application on thermo-mechanical system is relatively new phenomenon [Fraser 1998a]. 2.1 Thermal transfer function A thermal transfer function (thermal TF) contains the nature of the heat transfer principles, thus the calibration of the empirical parameters is simple and the model is in addition more reliable with untested inputs, because the data are forced to conform to the same principles as the real process. At the same time the results are obtained by two orders of magnitude faster [Fraser 1998b]. These parameters make the thermal TF very suitable for real-time modelling and diagnostics of varied thermo-mechanical systems. This topic is rarely discussed in a technical literature; therefore authors firstly created terminology used for thermal TF which is described in Tab. 1. The thermal TF can be employed for wide spectrum of application including diagnostics, determination of boundary conditions for a thermo-elastic FEA or a compensation of thermal errors at TCP, e.g. an inverse temperature transfer function (ITTF) is suitable for real-time heat source identification [Horejš 2009] etc. 2.2 Principle of the compensation techniques Thermal errors of a machine tool are result of a very complex thermo-mechanical process. In order to create high quality real-time thermal error model of a machine tool using transfer functions, these functions must contain dynamic parameters resulting from the current thermo-elastic state of a machine tool. The real-time self tuning of TF parameters will lead to a precise real-time estimation of current thermal errors. When these thermal errors are compensated, long-term thermal stability of a machine tool can be achieved. Compensation of thermal errors at TCP have been developed and experimentally verified on different real machine tools using two different compensation strategies. First method is based on control of the cooling systems which has to cause deformation right opposite to instantaneous thermal errors. This method is thoroughly described in [Bárta 2007]. This paper is focused on a second developed compensation technique using indirect software compensation. Principle of the method is shown in Fig. 1.