Even with compression couplings for the 1/2 inch copper, you will have to solder someplace. Soldering is not that difficult, if you follow the proper steps. Clean your joints, use pleanty of flux, and use lead free solder. The proper torch is the key. Most people buy a cheap propane torch to solder with, instead of propane use mapp gas and a mapp gas turbo tip. Home depo has the proper equipment. Then practice solder on a number of pieces before you start on the faucet.
But before you do all that. Have you tried disassembling the faucet and removing the cartridge. With all the parts out of the faucet, turn the water on and stand back. Many times you can blow out anything blocking the hot side. In addition, it may be the cartridge needs replacing. Often times pressure balanced faucets stop working on the hot side. Simply replacing the cartridge helps.
Of course you may be set on a new faucet. The old one may just be the first generation of pressure balance and not very good looking.