  Finite element models without simplifying assumptions can accurately describe
the spatial and temporal distribution of heat in machine tools as well as the
resulting deformation. In principle, this allows to correct for displacements
of the Tool Centre Point and enables high precision manufacturing. However, the
computational cost of FEM models and restriction to generic algorithms in
commercial tools like ANSYS prevents their operational use since simulations
have to run faster than real-time. For the case where heat diffusion is slow
compared to machine movement, we introduce a tailored implicit-explicit
multi-rate time stepping method of higher order based on spectral deferred
corrections. Using the open-source FEM library DUNE, we show that fully coupled
simulations of the temperature field are possible in real-time for a machine
consisting of a stock sliding up and down on rails attached to a stand.
