Thermo-mechanical models, based on the discretization of the heat transfer and elasticity equations, enable the analysis and optimization of the thermal design of machine tools. This work investigates the thermo-mechanical response of a five-axis precision machine tool to fluctuations of the environmental temperature. To increase the computational efficiency of the thermo-mechanical model, a surrogate model by means of projection-based model order reduction (MOR) is created. This article uses the parametric Krylov Modal Subspace (KMS) method, which enables the evaluation of the thermo-mechanical response of the machine tool for different values of the parameters describing the convective boundary conditions. The thermo-mechanical model is validated comparing the simulated and measured response of the machine tool to a step in the environmental temperature. The validation process uses the global sensitivity analysis (GSA) to determine the convective boundary conditions with the largest impact on the thermally induced deviations. The reduced-order model ensures the computational tractability of the Monte Carlo simulation associated with the sensitivity analysis and parameter identification. The validated thermo-mechanical model is used to investigate the thermo-mechanical design of the machine tool.