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 5-axis precision machine tool to fluctuations of the environmental temperature. In order 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 paper 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 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.