In most cases milky colored hot water is nothing to worry about. The milky coloring is only air and the water will clear when allowed to sit for a minute or, two.
The water coming into your home has many dissolved gases in the water that normally cannot be seen. Many gases can be dissolved into water such as atmospheric gases like oxygen, nitrogen, argon, carbon dioxide, hydrogen sulfide and other gases. In addition to atmospheric gases there may also be gases introduced into the water from water treatment such as chlorine, ammonia, and hydrogen depending on what treatment techniques your water provider uses. Finally in your water heater there is an anode rod, which reacts with the water and can produce hydrogen gas. The anode rod liberates higher amounts of hydrogen in its first year of operation when the water heater is new. The aerator on the end of the faucet spout also introduces air bubbles into the water flowing out of the faucet to make the water stream soft and prevent splashing.
The optimum situation for water to hold the highest amount of dissolved gases is when water is cold and under pressure. When water is cold the molecules are contracted and there is more room between them for gases to dissolve into the solution. When water is heated the molecules expand and very little room is left for gases, this is evident as you start to heat water to a boil on the stove and as it heats you see bubbles form on the sides of the pan. The pressure holds the gases in the water very much like a bottle of soda or, Champagne where you don’t see any bubbles until the cap is opened.
The water in your water heater has all these gases and is under pressure, but as it comes out of the faucet spout it is no longer under pressure and immediately the gases in the water start to come out of solution giving the water a cloudy or, milky appearance which will start to clear at the bottom of the glass first and gradually clear all the way to the top. This can happen with cold water as well but is much more likely to occur with hot water.
This is simply the tiny air bubbles rising to the top and releasing into the atmosphere. There is no need to worry about this happening it is completely normal and at different times of the year may be worse than others. If the water does not clear after 5 minutes you should check with your water provider or, if you are on a well get your water quality checked.