My radiator is a cappuccino. Would I have to remove the engine to deal with the headgasket?

1984 305trans am

 

No you wouldn't, need to remove the engine head gaskets are done while the engine is in the car.

It is not an easy job but it is doable, first you need to make sure it is a head gasket problem and not just a stuck thermostat causing the problem.

Remove the thermostat, and refill the radiator with water and run it a bit, if it does the same thing then look into a head gasket.

Don't leave just the water in the engine if you live in a cold area, make sure you drain it afterwards, or refill with 50/50 antifreeze.