Can I use hot water to transfer heat from a greenhouse into the house?
Pumping heat from the greenhouse into the room could be a feasible thing to do. Recall that the amount of heat transferred from one thing to another is proportional to the difference in temperature between the things. You've got four transfers in the proposed system (greenhouse air -&gt; radiator -&gt; water -&gt; radiator -&gt; indoor air) -- it might be a struggle to get good performance from that many transfers with only about 30 degrees F across the whole thing.
Instead, consider exchanging the air directly. Maybe you can conceive some blower door insert to place in the sliding door opening. You can get a damper &quot;off the shelf&quot; disguised as a clothes dryer vent, for instance. Place a damper up high to admit warm air into the room and another down low to admit cool air into the greenhouse. It might prove interesting to see how much heat transfers by thermosyphon alone, ie without any fan forcing the air to circulate.