I have this problem with one of my 80s. After replacing a blown headgasket, and several other items of indeterminate age, everything seemed to be OK, but the hood and fenders were too hot to keep your hand on after it had been driven for any length of time. The key data point was that this only happened when I drove in the mountains, and the transmission had been slipping (shifting later than the shift pattern, but still within drivable limits) before the blown headgasket.
In my case, I believe the worn transmission (I'm betting on clutch disks) is heating the coolant to the point that the fan can't keep up with it. The transmission cooling circuit runs from the transmission, to the lower radiator tank, and then to the transmission cooler, before returning. This means that a hot transmission will result in a hot engine, if the cooling circuit can't keep up.
If your transmission isn't shifting properly, especially from start under load, this could be at least part of your problem. It's important to thoroughly validate the function of the cooling circuit first, though.
I know my engine cooling circuit is functioning properly, because I'm the one who cleaned it and replaced all the parts. This leaves only the transmission as a source of heat. This 80 is a '95 model, so I have independent temperature validation, and I know that when the hood and fenders are hot, the engine is above normal operating temperature.
It's going to be difficult for you to independently verify the engine temperature while driving, since you don't have an OBDII port. Troubleshooting your problem, I would start at the thermostat, since a closed valve will cause overheating. Validate the part in a pan of water, as per the FSM, before just throwing a new one at the problem. If it's not malfunctioning, and you replace it anyway, you'll never know what the problem is. In my case, I know the valve works, because I tested it before installing it.
If your thermostat is good, the next suspect is the fan clutch, which should be tested too. If your water pump isn't leaking, it's likely not the problem. If both the thermostat and fan clutch are operating properly, you have to have your radiator flow and pressure tested. That's really all there is to the cooling circuit.