Thermal error plays a deterministic role in the machining precision of computer-numerical-control (CNC) tool machinery. Previously, three ways had been proposed to overcome thermal error problems: prevention, restraint, and compensation. The first two ways may be performed in the initial design stage. The last one includes the challengeable features of case-by-case simulation of cutting paths, searching for characteristic temperature points, thermal deformation measurement, and establishing an accurate thermal model. Different from most of the previous studies concerning mathematical thermal models, which have many restrictions and disadvantages, in this study, we propose a novel hybrid thermal error modelling scheme of the Grey system theorem and deep-learning neural network. Specifically, a linear-guide-way grinding machine, never seen in previous thermal-error-compensation-related studies, was chosen as the target to identify the usefulness of our proposed scheme. Results show that the proposed hybrid model has a comprehensive prediction ability of thermal behavior for the target CNC grinding machine.