<p>Thermal deformation is the primary cause of axial errors in machine tools. For accurate error compensation, it is crucial to quickly and accurately obtain the thermal characteristics. In most conventional prediction and compensation methods, the heat generation rates and convective values are dependent on empirical formulas and data, which cannot consider the time variation and randomness of the external environment and internal system. This leads to large calculation errors and low calculation efficiency. Additionally, the description of the temperature field at large temperature gradients in complex systems is insufficiently accurate, and the redundancy of thermal nodes at small temperature gradients cannot be eliminated. This study first establishes a universal unit adaptive thermal network model for dynamic mobile thermal excitation, which is used to solve the heat transfer problem considering time variation and randomness in practical engineering. It adaptively adjusts the scale and number of thermal units to improve the computational accuracy and efficiency of the thermal network. Furthermore, a new compensation framework for thermal errors is proposed, considering the time variation and randomness in practical engineering. Finally, compensation experiments for the thermal errors were performed using the proposed methods. Using the presented models, the time-varying performance of the system and the random impact of the working environment can be automatically identified, and the real-time transient temperature field of the machine tool can be captured. The experimental results show that the proposed thermal network models and thermal error compensation frames are effective under time-varying and random external environments and internal systems.</p>