In traditional machine tool thermal error detection, eddy current or capacitive probes are mainly used. We propose a new data sensing architecture consisting of two main components: a thermal error sensing model and a temperature sensing module. The thermal error sensing model is composed of two quadrant detectors forming a 3D displacement error sensing module. The temperature sensing module consists mainly of multiple PT100 sensors. In the thermal rise experiment, spindle XYZ directional thermal errors are detected by the displacement error sensing module, while temperature changes at various locations are detected by the PT100 sensors. The experimental results show that the main thermal errors of the spindle are in the YZ direction. Therefore, we introduce four neural network algorithm methods [Temporal Convolutional Network (TCN), Generative Adversarial Network (GAN), Long Short-Term Memory (LSTM), and Bi-directional LSTM (BiLSTM)] to establish various models for predicting the spindle’s thermal errors in the YZ direction. The predictive results indicate that Z-direction predictions are more accurate, with model accuracy maintained up to 70% after six months. In the Y-direction thermal error model, significant improvements in prediction results were observed after the RPM parameter was incorporated into the model. Among the various models compared, TCN and BiLSTM show the best performance in terms of accuracy over extended periods and across different thermal error directions.