I have had a rug over top of a heat vent for a while, but I wanted to make sure it is safe.
sure, close it if you can or cut a piece of cardboard that fits the vent to block it
I think you must be talking about a heat vent on the floor. I have one in an upstairs bedroom and had to have the carpeting cut around it when I re-did the room. The l heat vent is 12 inches square. The workers did a great job with the new carpet and the vent does not look out of place.
It depends upon what kind of heat vent you have. If it is a floor furnace, it would get hot enough that it could start a fire. If it is a forced air heating duct, the rug would prevent the air from coming into the room, but the temperature of the air coming out isn't high enough to cause a problem. If it is a forced air heating duct, you could pull the register out of the floor, cut a hole in the rug the same size as the duct boot and slip the register back into the hole so you would have the warm air coming into the room.