Injection molding using inserts from vat polymerization, an additive manufacturing technology, has been investigated for pilot production and rapid prototyping purposes throughout the past years. A standard mold is equipped with additively manufactured inserts in a rectangular shape of (20x20x2.7)mm3 produced with vat photo polymerization. While the lifetime compared to conventional materials such as brass, steel, and aluminum, is reduced, the prototyping and design phase can be shortened significantly by using flexible and cost-effective additive manufacturing technologies. Higher manufacturing volume still exceed the capability of additively manufactured inserts, which are overruled by the stronger performance of less-flexible but stronger materials. This contribution discusses the heat transportation within the inserts made from a thermoset material, brass, steel, and ceramic material. It therefore elaborates on the possibilities of injection molding as well as the thermal challenges connected with the use of polymer inserts. They are an essential part for further calibrations of the injection molding process. The numerical simulations were conducted using the Comsol Multiphysics® version 5.3 Modules for laminar fluid flow and heat transfer as well as the multiphysics model for non-isothermal flow. The interface between the flowing and cooling injected material was approximated by applying effusivity between the materials. The high interface temperature due to the effusivity of the photopolymer, cooling required a higher heat transfer into the mold and surrounding. The conventional mold showed only slight temperature increase whereas it needs to be considered that the overall heat capacity of the steel mold is significantly greater than the inserts. An influence of the inserts on each other was therefore not detected which allows for further prototyping techniques, e.g. a reference insert while the other inserts are changed during the prototyping development.