Our two-story A-frame house only has duct-work downstairs in the crawl-space, with vents in the floor. It gets quite hot upstairs during the summer, but because the square footage of the upper floor is less than downstairs, we were thinking it might be more economical to go with a through-the-wall air conditioner upstairs. But I'm a big fan of the Nest thermostat, so I'm trying to find an A/C unit that would accept an external thermostat. Any ideas where to start? Google just arbitrarily decides whether to apply "wall-mount" to "thermostat" or "air conditioner" but not to both.
SOME models of the GE AJCMxx, AJCQxx, AJEMxx, or AJEQxx has the ability to wire in a standard 24 VAC "Class 2" thermostat. It is explained in the manuals, which I believe you can download from GEAppliances.com.
I wish I'd thought of this myself when I bought my through-the-wall A/C - it's bound to be better than the internal gas-tube thermostat.
You should at least consider talking to an A/C person. Assuming your existing unit is big enough, you may be able to just run a duct line up to the 2nd floor. Generally they box in a 1ft square in the corner of a room or closet to run the ducting.
Beyond that, I do know some through the wall units work off thermostats, because I've seen them in apartment buildings around here. I've also seen mini splits hooked to thermostats in hotels, so I'm sure that is possible as well. Usually they will have the little control unit on the mini split sealed shut with a note telling you to use the thermostat.
Let me see if I understand this. In warm season no air, or not nearly enough air in the upper floor space is returned via the vent to the exchanger one the ground because the only return vent is situated somewhere on the first floor...so that cool air blown up through floor registers cools the large ground floor space (where the cool air tends to sink) but is "captured" by "suction of the return vent before it has any chance to arrive at and transfer heat from the upper floor (where, in addition to heat rising and being captured there, heat is is also conducted inside via the roof/wall. So what you have, essentially, is an upper floor (conductively importing heat) that is isolated from the centrally air conditioned part of the house. Or, you have the house (especially the upper floor space) so air tight that excess warm air rising a-frame-apexward, both or either, is too much for a top floor return vent to handle, or cannot escape the upper floor volume by another path.
So let's see if any fundamental things have been tried or considered. Have you tried cracking open a window in the upper floor to see if some rising hot air escape allows at least some improvement cooling the entire house? Have you looked into the possiblity of moving or adding the/a return vent to the upper floor so that it is not isolated from the lower floor? Maybe such a return path could be in the form of an external ductwork "stack" directing air into which heat has been transferred upstairs, back down to the exchanger on the ground?
Additionally, are there dampers down in the crawl space duct work with which, but way of "balancing" the floor registers, you could assure that the most cooling air is always delivered to the register(s) closest to a an open path (think stair well, spiral case, ladder, etc, or even ceiling-floor grate path(s) to the upper floor space? Or, if not dampers in the ducts, then are the floor registers' flows, themselves, adjustable?
Another thing. To what end would you need the window/wall unit upstairs controlled by a wall thermostat? Are you thinking of controlling the windor/wall unit from the main, central air t-stat? If so, would you not have the same bad situation...because the upper wall unit would never turn on...bacause its integrated t-stat is removed from any cycling loop?
In order for the central and the wall unit not to work against each other, simply isolating the upper floor from the lower (closing doors or ladder openings, say) would allow the wall unit to cool the upper floor with its own integrated thermostat whenever the upper floor needed to be occupied. By Central-Wall Unit conflict I mean that the return vent from first floor back to the exchanger will be likely to also draft air (away) from the lower-tonnage unit upstairs...so you have the upstairs unit starved off enough recirculating air...the result of which could be dimished cyling off of compressor, with proportionally higher electricity consumption and expense for for the desired amount of heat removal augmentation upstairs.
Another option than a 24VAC thermostat is to use a line-voltage thermostat to switch power to the unit entirely.
One variant is a plug-in type (such as this one).
There are hardwired versions for heating, they may also exist for cooling.
I'm not sure how the NEST works specifically but if it has a line-voltage version that might work for this also.
Similar to this answer there is a mechanism to use a 24 VAC thermostat, even if the AC unit itself is not directly compatible. You can use a contactor controlled by a thermostat to switch the power to the A/C unit. I have seen several hookups of this type for electric heating and I think the same principle would work for AC.
Note -- A contactor is basically a robust relay (electrically actuated switch) which can handle the full 120 (or 240) volts & current of a larger appliance.
You would want to give some thought to the "deadband" setting of the thermostat to make sure the AC unit wasn't switched on/off too frequently which could damage it or shorten its lifespan. Deadband is the difference between the on and off setpoints of the thermostat. e.g., if you set your stat for 70 F in reality it may switch ON at 71 and OFF at 69. (This is also known as hysteresis).