Thermal deformation is the main factor affecting the machining accuracy of grinding machines， which severely limits further improvements in the accuracy of machine tools. However， only a few studies have investigated thermal error prediction， and the prediction accuracy has been low. Therefore， this paper proposes a method to predict the thermal error of grinding machine spindles based on the heat conduction theory and a convolutional neural network. First， according to the heat conduction theory， the mapping relationship between the thermal variables and the temperature difference between the surface of the main axis of Chu and the external environment is deduced， revealing the thermal deformation nature of the materials. Second， a neural network model for thermal error prediction with temperature difference as the input and thermal deformation of the main shaft as the output is established. The model has four neural network layers corresponding to temperature difference， thermal energy increment， time variable， and thermal deformation. The back-propagation algorithm is then used to train the prediction model and calculate the model parameters. Finally， based on the SINUMERIK 840D CNC controller， a set of thermal error compensation systems for grinding machine spindles are developed and verified using a CNC grinding machine. The results show that the machining accuracy of the grinder is improved by 41.7% following thermal error compensation for the spindle， thus confirming the validity and feasibility of the spindle thermal error prediction model proposed in this paper.