We live in a three story house, with our bedroom in the third story loft. On sunny days, it gets too warm up there, even with the windows open (not to mention the neighbor’s 4:00am rooster crowing). The bottom floor (ground level) is heated with a mini split, and also has our heat pump water heater in the laundry room (no door, but at the opposite end of the level from the heat pump). As a result, the laundry area is always very cool. What is the downside of putting in a small mini split with the indoor unit in our bedroom, and the outdoor condenser in the laundry area? I would then be using the warm 3rd story bedroom air to heat the laundry area/ heat pump water heater, and the cool laundry air to cool the bedroom. Thoughts?
Big commercial multi-zone systems (like Mitsubishi City) actually do this sort of thing internally. They'll move heat around from one indoor unit to another as needed, and only go to the outdoors for heat that they can't get from somewhere else in the system or can't dump to somewhere else in the system.
I believe the Chiltrix units also do this sort of thing, by supporting using the waste heat you pull from rooms as a source of heat for hot water.
What you're proposing is basically a less flexible version of those systems. It won't work if you ever want to heat your third floor, rather than just cool it, since then you'll have all your devices pulling heat from the laundry room. You will also have to worry about condensate management at the outdoor unit if that ever happens. But apart from that, I'm thinking it should work. Something similar is pretty common in warehouses with offices inside of them. The office will have a mini-split installed with the outdoor unit inside the warehouse. It works just fine.
Before I spent that kind of money, I would get a duct booster fan and a bunch of cheap flexible duct to force the cool air from the utility room up to the bedroom. Temporary and ugly, but it might show that the cooling capacity of the water heater is insufficient.
An overall better idea is to put in a multi zone mini split system. Some are capable of closing a valve in the outside coils, thereby moving heat from one air exchanger coil inside to another.
Bad idea, when compared to the idea of putting the outside unit outside.
Because then, you have an all-season heat/cool system that doesn't affect other rooms, and is able to serve as a backup to the downstairs unit. Think winter and the downstairs unit conks out, you can still heat the house via the upstairs unit and leaving doors open and maybe a fan in the doorway. If you were heating the bedroom by stealing heat from downstairs, that would not work at all!
Maybe add a fan to stir the air in the downstairs area so the cooling effect of the HPWH is distributed throughout the 1st floor.
I agree with longneck, that the proper answer is a multi-zone heat pump equipped to move heat between zones. In fact one of those zones could be an air-water heat exchanger inside a hot water tank, i.e. the HPWH being one zone.