Yes, if you can carpet it all, even with a thin carpet, that should help a lot. But acoustic tile is cheaper than carpet. You can glue it to the plaster with construction adhesive, in tubes that you load in a caulking gun. Of course you'd need a tall stepladder.
If there's no return air grille in the room, then the return is through the door louver and along the corridor to another louver at the furnace room. They used to do that a lot. You could screw hooks into the door just above the louver and make a panel that hangs on them. It can be anything heavy. Try to get it to seal around the louver frame when it's in place, maybe with foam weatherstripping.