An assembly is provided for a turbine engine with a flowpath. This assembly includes a fuel source and an engine component. The engine component forms a peripheral boundary of the flowpath. The engine component includes a component internal passage. The engine component is configured to receive fuel from the fuel source. The engine component is configured to crack at least some of the fuel within the component internal passage thereby cooling the engine component and providing at least partially cracked fuel. The assembly is configured to direct the at least partially cracked fuel into the flowpath for combustion.