The material the cover is made from does not impact the efficiency of your heat. Being an insulator, a wood based cover will allow more energy to be passed to air molecules rather than the enclosure which has little effect on efficiency, but does affect slightly the speed in which the air in the room is warmed. The cover is simply an enclosure which directs the convective flow outwards toward the center of the room. This does 2 things, keeps the flow from travelling up exterior walls, which can pull in cool air through gaps around windows, etc. and helps the more energetic air molecules disperse energy to those in a lower energy state (cooler air) a bit quicker. The system transfers heat from the fins and pipe to the air directly, passing energy to those molecules which become less dense, in turn creating a convective cycle through the molecules with a lower energy state (more dense). The air in the room will find an equilibrium in energy. This happens quicker with more air flow in a space since this process is in effect a chain reaction between each molecule contacting another. The cover helps this happen since it creates turbulence towards the center of the room instead of a column of warm air that disperses at the ceiling. In a well sealed room, you can take the cover off altogether with no difference in the amount of energy transferred, but the speed in which equilibrium is achieved will be a bit slower