Cartridge Issues
The cartridge is the valve inside the faucet that regulates the amount of water that flows out of the faucet and the temperature of that water. Each cartridge has inlets for hot and cold water. When the handle turns, it aligns the inlets so either all hot, all cold or a mixture of both comes out of the faucet. If the cartridge is damaged, or not lined up properly, you will not receive the proper temperature water. Sometimes hot water comes out when cold is supposed to flow, for instance. To fix the problem, shut off the faucet water supply under the sink, take off the handle and replace the cartridge.
Supply Lines Crossed
Two supply lines feed the water to the faucet -- one supplies cold water from the cold water pipes, and the other supplies hot water from the hot water pipes. If, by chance, you connected the hot water pipe to the cold water inlet on the faucet, you will receive hot water when you operate the cold water handle. If this is the reason your cold water is running hot, you will also get cold water when you turn on the hot water handle.
Fixing Crossed Supply Lines
To fix a set of crossed supply lines, you simply swap the lines. Before doing that, however, you must turn off the water under the sink. Shut both valves on the water pipes by rotating the valve handles clockwise until they no longer turn. Unscrew the connectors on the water pipes, switch the connectors to the other pipes and tighten each one. Your hot water pipe now should supply the hot water side of the faucet, and the cold water pipe should supply the cold side.
Hot and Cold Pipes Crossed
Less likely, but a possibility nonetheless, is a mixup in your home plumbing situation. Your home may have the hot water pipe on the right, instead of on the left, where it typically is. Whoever installed the faucet connected the right hose to the proper side of the faucet, but failed to realize that hose was supplying hot water. To determine whether this is the issue, place your finger on the pipe on the right side -- that is, the pipe supplying the cold water side of the faucet. If it is hot, your pipes are on the wrong side. Simply switch the supply hoses.