The heater core will need to be replaced. Normally the air conditioning system will need to be discharged so the heater box can be removed from the truck. There are some Dodge trucks that have heater boxes that can be partially split in the front and the heater core snuck out that way. Don't know if that applies to your truck.
The problem with driving this way is the irritation of an oily film settling on the windshield and the potential for engine overheating. Keep an eye on the coolant level in the radiator and reservoir. In cooler weather, you might get away with leaving the radiator cap loose to prevent it from building pressure. As a last resort, you can remove the two heater hoses from the heater core pipes at the firewall and connect them together with a plastic splice connector and two hose clamps. That will bypass the leaking heater core. The leak will be gone, but you won't get warm air from the heater.
Sunday, March 14th, 2010 AT 2:12 PM