2001 Dodge Truck smoke

The heater core can be bypassed by taking the two hoses going to the heatercore disconnect them and get a short piece of metal tubing that will fit snugly into them and connect them together with hose clamps. Although your heater will no longer blow hot air.
Also I dont think the heater core is the problem. The heater core is supposed to be warm as it takes the hot engine coolant and circulates it through it so when the air is drawn through it it heats the cab.
What did it smell like? Did it smell like electrical burning? If so check all you fuses to see if any are blown whatever fuse is blown will help to locate what may have been burning