Should it be that a radiator or expansion chamber not be defined as a cooler reseviour then the law is wrong not the workings.
?? If you have a warm reservoir and a cooler reservoir then your heat engine can work as long as that differential is maintained against the heat that your engine is transferring into the cold reservoir. This is basic thermo.
If you imagine you can dump the heat into the reservoir and then magically remove it, then you have a Type 2 perpetual motion machine.
See "Einstein" Ammonia absorption fridge.
It is a refrigerator that gains its energy by using a heat source (like a flame) that transfers heat to a heat sink (the environment.) As long as you maintain that temperature differential it works. If the environment ever rises to the temperature of the flame, it ceases operation.
The Wikipedia article is a good overview, and includes this note:
"The absorber works by removing ammonia vapor by dissolving it in water. As this happens, the gas mixture flows to maintain the nearly constant pressure Psys, and as a consequence, the partial pressure of the refrigerant, Prfr, can approach Psys. At this higher partial pressure, it can condense and deliver heat to an external heat sink, as in a conventional refrigerator."
That "external heat sink" is the critical part, and is the reason that your device will not work.