Local building codes are one of the first things that you have to check before you even consider putting up a wall to conceal to your furnace and hot water heater. Local building codes may require that you use certain types of materials or may make specifications regarding the distance of the wall from your heater and water heater. You don't want to put up a wall only to find later that you have to take it down or pay a hefty fine because it doesn't meet legal specifications.
The distance of the wall from your furnace is also one of the primary considerations you need to make when building your concealment wall. Your wall will need to meet the minimum code requirements for your local community, but it will also need to provide enough room for service technicians to be able to work on your unit. The general rule of thumb for determining distance is to measure the depth of your unit and create at least that much space between the wall and the furnace and water heater. Therefore, a 36-inch furnace should have at least 36 inches of additional space between itself and the wall.
You will also need to be code-compliant in terms of the materials you use to construct your wall. You will need to purchase fire-rated drywall that is the highest quality possible. If there is one area of home improvement you shouldn't skimp on, it's the fire retardant material that you use to construct the walls around your furnace and water heater. If local code calls for a minimum thickness, exceed the minimum standards to help ensure safety.
Construction of a wall around your furnace and water heater may be an expensive and difficult venture to pull off. You may wish to consider some alternative strategies before diving in head first into a project that may overwhelm you. For instance, portable and decorative room dividers can easily be used in place of a permanent wall, as can louvered doors. Avoid using curtains or other flammable materials that may sway in the breeze. These can be a dangerous fire hazard.