The heater core lines are stubbies that just stick out the firewall a couple inches. When the heater hoses are connected they slide all the way up, giving the appearance that they go through the firewall. If your core is leaking it is an indication of really poor maintenance being done by the prior owners. My heater core is the original. I suspect your radiator will be leaking soon also.
I'm curious about the top radiator hose being cold. You are talking about the one into the radiator, right?
I'm curious about the top radiator hose being cold. You are talking about the one into the radiator, right?