I have a gas burning fireplace. Can I close the slu to keep the heat in?

No, you run a serious risk of suffocation if the flue is closed. Natural gas is a hydrocarbon made mostly of methane. When methane burns, the natural byproducts are carbon dioxide and water vapor. Carbon dioxide is heavier than air and can displace oxygen. The result is lack of oxygen and suffocation. Also the water vapor will condense when the gases of combustion cool. The gases of combustion require a way to get out of the house. As the gases rise oxygen in the air is naturally drawn in to mix with the natural gas being burned. A closed flue will interfere with the natural tendency of the hot gases to rise, and that can result in not enough air mingling with the natural gas. When there is not enough air reaching the natural gas, incomplete combustion will occur. Incomplete combustion produces carbon monoxide which is a deadly poison. It attacks the soft tissues of the nasal pages, the lungs, the heart and the kidneys. It also destroys red blood cells. Carbon monoxide poisoning is very difficult to recover from.