The heater core is located under the hood in the heater box where the blower motor is. Remove the heater hoses then the box can be unbolted and removed.
There is a valve which controls the flow of coolant to the heater core, which is a small radiator located inside the passenger compartment. If this valve is open, hot coolant will be pumped into the heater core, which will get hot and warm the air passing over it. If the lever or temperature selector in your vehicle does not control that valve, then the cable is broken, or the electrical control device is not working.
To replace the battery on a 1979 Corvette, disconnect the battery cables using the proper tool. Remove the bar that holds the battery in place and pull out the battery. Place the new battery in and reconnect the cables.
If this is the original heater core it may be stuck to the firewall and you will have to pry it off. Make sure that there are no other bolt holding it!!!
Not without modification
I am not sure, but it sounds like your heater core may be leaking. You may be lucky, and only have a hose leak. But most of the time its the core that goes bad and needs fixed or replaced. You may check under your hood and look at the two hoses that go into the fire wall on the right side of the car. If your lucky one may be leaking at the clamp and only need to replace that clamp. But most of the time it will be the heater core in the fire wall that's the problem and need's replaced or fixed. If you need to drive the car before getting it fixed. You can take both the hose's off the core at the fire wall. And connect them both together with a two or three inch pipe and two clamps. This way you can still drive your car until you get time to have it fixed. Be ware though that by placing both hoses together you will not have a heater. Good Luck M.C.S. The Missouri Crack Shot.......
there are 15 crews on a 78 and 79