If a system absorbs heat and also does work on its surroundings its energy

This is, I think, about heat engines and the first law of thermo? Hot reservoir supplies heat to the system at a high temperature. System does work. System rejects some heat to a cold reservoir at a low temperature. That's a word description of a thermo block diagram. And I think it refers to the "steady state". Seems reasonable that the system would have to warm up (car engines, eg), during which process the (internal?) energy would presumably rise. In the steady state, however, the energy will presumably be constant. If it continued to rise ... the thing would overheat?