Machine tools are susceptible to a wide range of thermal field variations that result in thermal deformations or positional deviations of the tool center point (TCP), which affect the manufacturing quality, life cycle of the tool, and production time. Therefore, accurate thermal and thermo-elastic predictions play a significant role in satisfying the manufacturing demand for precise machine tools. Finite Element Method (FEM) based correction of the thermal deviations of the mechanical systems is a very energy-efficient strategy. However, those are computationally expensive, especially for large-scale simulations. Model order reduction (MOR) techniques are applied to reduce computational costs. However, little attention is paid to instruct clear guidelines for the optimal MOR technique for specific boundary conditions and types of problems. To address such a problem, this paper compares two Krylov subspace-based MOR techniques regarding their computational efficiency and accuracy. Therefore, the study examines two levels of model complexity: a bar-slider and a test bench. For both cases, the thermal computational time is compared with and without MOR. Finally, proper guidelines are established to select the optimal MOR. It is observed that MOR using the moment matching method is more computationally efficient and accurate than the Arnoldi iteration.