The consistent application of method of vertical lines yields after the spatial discretization of the balance of linear momentum and the local balance of energy (heat equation) a coupled system of differential equations (ODE) and algebraic equations (in the absence of inertia terms), which represents a system of differential-algebraic equations (DAE). If the constitutive model is accompanied by evolution equations, additional ODEs have to be considered. The entire DAE-system is solved here by diagonally-implicit Runge-Kutta methods, where higher order methods are possible and time-adaptivity is more or less for free. Several approaches using high-order in space and time for the case of large strain thermo-viscoelasticity, thermo-viscoplasticity for quasi-static, and dynamical approaches have been discussed in the literature. For the case of chemo-thermomechanics of curing processes it becomes slightly more delicate since the curing model is inherent unstable. Thus, high-order time integration is a must. This is discussed in more detail and particular applications are demonstrated.