The bath/shower faucet is the type that is just a single handle. 6:00 position being off; 9:00 position being all hot. But only hot water is coming out. It was working properly when we purchased the house (built in 02) and worked up until I don't know when as it's rarely used. Mostly by guests. The cold water does work at both faucets in that bathroom. What could be the problem? No brand name visible or logos, etc.

Brand name? Temperature control? Can you furnish more details? Back to you, Tom

Replace cartridge. They are inexpensive and will solve your problem without guessing. If you still want to try to fix it than turn off water, remove cartridge, clean it real well and reinstall. If the cartridge show signs of calcification than you have to dip it in household vinegar and hope that will help. There is 50/50 chance it will.

Hope that helps

Milo