One of the plumbing experts may chime in with a better answer, but my guess is that (assuming you DO have hot water) that there is an obstruction somewhere in the hot-water line that feeds this faucet.
If you take the faucet apart, you can examine the seal on the hot side to see if it has clogged up. (Make sure you shut off the water first!)
I would bet the problem is in the faucet, but you can't guarantee that.
Here is a picture to give you a rough idea of what you're looking at.
Good Luck,
WallyH