Thermally induced deviations are a major contributor to positioning errors in machine tools, significantly impacting machining precision. This paper presents a model-reduction-based temperature field reconstruction method for volumetric error compensation. The temperature field is interpolated between temperature probe locations using projection basis vectors obtained through model order reduction of finite element models. Thermal effects such as convection are modeled as external heat loads, allowing their influence to be incorporated without requiring exact heat transfer coefficients or fluid temperatures. The approach allows thermal errors to be evaluated at arbitrary positions in the machine’s kinematic range, facilitating volumetric error compensation and integration with numerical compensation strategies. Experimental validation shows a good agreement with measured displacements. Maximum deviations of 19  \(\upmu \) m were observed, while the maximum reconstruction error is 1.1  \(\upmu \) m. The method’s computational efficiency and real-time capability make it a scalable and robust solution for model-based thermal error compensation in modern manufacturing machinery.