Through-the-wall A/C that works with external thermostats

There are a few things you can do which can help:

1) Adjust the dampers in the duct work. Partially close dampers in the ducts going to the first floor and fully open the ones to the second. Take some time to mark them so you know what goes where. It will probably take a few tries to get them set right. That's usually the first thing an HVAC guy will do for this situation.

2) Seal off the leaks in your duct work. Go around and find leaks and seal them with the aluminum backed tape. It's real sticky and has a peal off backing. Oddly enough, duct tape always seems to come loose on my duct work. Go figure. There are services which will come out and blow a smokey substance through your system to locate leaks and seal them.

3) This can be controversial, but you could cover your low returns in the summer and high returns in the winter. The theory is that this will pull more warm air out in the summer and more cold air out in the winter. There are magnetic covers you can get for this purpose like this:

But you may have better luck with stronger magnetic sheets and custom cut them yourself.

I'm not a fan of closing registers, but that's probably one of the simplest things to do.

There are systems that can be installed which will automatically adjust dampers in your duct work based on thermostats placed throughout the house, but they're pricey.

Heating and air conditioner units have a fan that pushes air and it has a maximum ventilation capacity. The air return “allows” the air conditioner to draw air back into the system and is called “make-up air”.

That is to say, the fan can only “push” so much air, whether you’re heating or cooling and your unit will draw the same amount of air back into the system.

If you are “cooling” the basement too much and not cooling the upstairs enough, then you want to distribute more air to the warm areas. This is called “balancing the system”.

Without re-sizing all the ducts, you could cover the “supply” vents in the basement, which will force more air to the other areas. (You may be able to just partially close the downstairs vents, if you have adjustable vents.) By redistributing that air to other areas, those areas my get too cold, so you’ll need to “balance” the system by adjusting those vent covers.

During the cooling season, we like return air vents where we can bring cool air into the system and re-cool it to the desired temperature. (Likewise with the return air for the heating season, we like to have warm air returned to the system so we can re-heat it.)

I doubt if you have 2 return vents, I’d just cover some of the supply vents in the basement until it’s comfortable.

BTW, by covering some vents, you are forcing more air into other ducts. If those ducts are too small to “handle” the additional volume, you’ll hear a slight “whistle” sound. If so, you’ll just have to re-adjust how many vents you cover in the basement.