a new radiator from rock auto isn't all that much money and they aren't terribly difficult to install. if you like the car otherwise, it will give you peace of mind.

30+ year old radiator...I'd bet it's clogged, because from what you've described and done, there's no flow. And if it's not the radiator then there's blockage somewhere else.

Hey bud, hello from California. I have a similar story from a 1989 civic I bought a few years ago. I also bought it with a known overheating condition. I was hoping it would be an easy thermostat or radiator fix but I ended up needing to overhaul alot of other stuff like the head gasket. The gunk on or around the engine does not really affect heat dissipation and can even help to jimmy fix small oil leaks. Really it's your radiator that you have to focus on and the potential rust or corroded surface of the inside of your engine that makes contact with the coolant. You are on the right track with checking the temps around the radiator. Those IR temp guns go for around 15usd these days and can do the job of testing the radiator hose at the inlet and outlet. If you are out of spec you should just replace it, no flushing solutions that I know of perform as well as a full radiator replacement which is around 100usd in parts for your car. Mine was 43usd for the civic and was a pretty easy fix.

I was driving on I-40 trusting it would make it to the Cars and Coffee in Knoxville. I almost made it then my car radiator had a hole in it and was spurted coolant in everywhere. On the bumper on the grill, some on the bottom of the hood. So Answer is Radiator. 😀 😀 

Check to make sure your radiator fans are working......