I use an AC unit in my chamber, too. I agree with MCL that doing lagers would be better in winter months or the unit will have to work very hard and you'll be paying for it in energy costs. My AC unit is quite old and, therefore, not super energy efficient but it could maintain 50* in the summer. I wouldn't do it where I live, though, as it would be cost prohibitive.
For a while, I used the thermostat on the AC unit to adjust temperatures but the AC would run the fan constantly as long as the unit was plugged in, which got expensive and annoying. Since then, I wired in a Johnson temperature controller and it has made a world of difference. The chamber has a much more stable temperature and the ability to program various particulars with the Johnson controller is really nice. I know that the thing has paid for itself in terms of the savings on energy costs.
Also, when you get yours built, load it up. The more carboys and kegs you can stick in there (that are full of liquid) the more thermal mass you'll have to insulate and regulate temperatures. Mine is two tier to take up less of a footprint, which I like, but that might not be practical with a conical. There's a nano brewery nearby where I live (Hess Brewing) and he has a couple chambers built to house his conicals--he could be a good source of info, too, and is likely a quick internet search away.