Start with the easy stuff first and make sure the electric fan is coming on when the AC is on.
If not, and you know your way around basic 12v wiring, you can pull the two relays that are in the engine compartment fuse box near the battery, and jump pins 30 (always hot from battery) and 87 (output)with a short pice of 14ga wire shaped into a U, or even a paperclip. If the fan didnt work before, but now runs when you jump the relay, then the relay is bad. Then when you jump 30 and 87 on BOTH relays at the same time, the fan speed should increase. Thats how the fan is supposed to work on AC. If the fan still doesnt run, then you need to dig deeper.
That said, my AC didn't cool even though it had a full charge, until I changed the AC condensor in front of the radiator. The fins can get corroded, or filled with crap, either of which seriously reduces cold output by blocking fluid to air heat exchange. If the condensor is dirty or corroded enough, it can also lead to not enough air flow to the radiator, which, you guessed it can then lead to engine overheating.
After I changed the condensor and drier/accumulator and all the lines ( once you break open the AC system, you might as well start replacing the parts and o-rings that are gonna start leaking soon enough), then Giddyup's AC started working perfectly…well at least once she was properly recharged and oiled.
NOTE that the AC condensor, at least on a CRD, has the ****** cooler built into the bottom of it and if you dont get the right aftermarket one, which is seldom available, then you need to add a smaller separate transmission cooler as well, which involves changing some plumbing around.
I DO have a brand new extra Nissen cooler that has the built in cooler that I could sell you at cost plus shipping if you need it.