I've got a classic air in my 12v 55 Thunderbird. Rotowrench is right about the power requirements. You just don't add a bigger alternator, you've also got to increase the wire size from it to the battery (I'm ignoring a generator set up, the regulator, etc. I wouldn't use the existing 6 volt wiring, while the size might be ok, the condition of the insulation probably isn't). The classic air instructions are lacking in a couple area, and there's some wiring check out you need to check on the bench. Or you get to take it out to fix it, at least in a bird. The water control valve is also a problem, despite being installed properly.
I'm runnning a BeCool aluminum radiator with a large electric fan and close tight shroud. Cooling at 90+ in Seattle is ok, but the condenser fan is marginal at that point.
I've got an OT 67 with a vintage air unit. It works probably as well as the oem units did, uses all the factory controls and layout. It has a larger BeCool radiator laid out as Kultulz suggest. Two big horizontal fans, one comes on with the a/c, the other on engine temp (or both staggered on temp if the a/c is off. But it's an integrated computer controlled system on a later model EFI engine. Stuff just not available for Fords unless you build your own.
I always found the factory heat and defrosters fine in the bird, and sometimes I wish I hadn't replaced them. In a full size car I'd use an add on under dash unit way before I used an integrated one. Not knocking either manufacturer. The bird is tight on underdash space and legroom and after sitting a a friends 57 bird (with the under dash) I made my own choice.
If I'd had the ability, I'd have built some kind of an underdash "waterfall/console/ whatever" and used individual parts to complete the system. But there's some pretty period correct underdash units out there.
Here's the VAir one. Kind of hard to find on their main site.
https://www.vintageair.com/universit...ersal-systems/
This is how my center vents ended up on the bird, custom cast panel from Ace in NZ.