You could "Rube Goldberg" a design using 2 heat exchangers, small pump, and antifreeze. You could hang a transmission size cooling radiator in front of the exhaust on the outside, have 2 flexible insulated lines running to the inside, to another radiator/heat exchanger with a small fan moving air over it. A small pump to circulate a non-toxic coolant and you would have a heat source in the basement. Wire the pump and fan to come on with the furnace relay.
As others have mentioned you cannot restrict the exhaust heat, so I wouldn't cover it or box it in.
My opinion only
