A modelling strategy for the prediction of both the scalar and the position-dependent thermal error components is presented. Two types of empirical modelling method based on the multiple regression analysis (MRA) and the artificial neural network (ANN) have been proposed for the reaLtime prediction of thermal errors with multiple temperature measurements. Both approaches have a systematic and computerised algorithm to search automatically for the nonlinear and interaction terms between different temperature variables. The experimental results on a machining centre show that both the MRA and the ANN can accurately predict the time-variant thermal error components under different spindle speeds and temperature fields. The accuracy of a horizontal machining centre can be improved through experiment by a factor of ten and the errors of a cut aluminium workpiece owing to thermal distortion have been reduced from 92.4 Ixm to Z2 lazn in the lateral direction. The depth difference due to the spindle thermal growth has been reduced from 196 txm to 8 ~m.