To solve the multiscale problem of additive manufacturing of large components by material extrusion (MEX), this work utilizes the methodology of submodeling and shows the necessary modeling steps to apply the methodology to the material extrusion process. The research enables the coupling of high-resolution models and process simulations at the component level. It allows the investigation of local effects such as crystallization effects or the resulting interface strength and its dependence on process variables in critical zones of a component, considering the component geometry as well as global and component-specific process conditions. The principle is verified numerically and validated experimentally, showing good agreement. In addition, different specifications for boundary conditions and submodel sizes are compared and evaluated. Variable time increments are used to apply the submodels with a computational time independent of the component size. In addition, sensitivity analyses provide information on the necessary temporal and spatial discretization of the submodel for the most accurate prediction of the temperature profile.