First I would check the shut-off valve under the sink or wherever it might be (basement, access panel). Is it/are they all open all the way. If open, then try pulling out and cleaning the valve stem on the faucet. Make sure to turn off the water first. Also check for kinks in the water lines. Hope this helps.
Have you recently shut off the main water? Sometimes shutting it off can dislodge sediment or buildup, and it sometimes will settle in the shutoff valve at the fixtures. I would suggest shutting off the water, and then disassemble the shutoff valve with a crescent wrench. Make sure there is no sediment in the valve or where the supply line connects to the valve.
If your issue is only confined to the hot water in the vanity, then it is most likely an issue from the valve to the faucet.
Check out superhandyman.com He has a great procedure for that exact problem.