Welcome to the forum.
There are several things that you need to check out on the overheating issue. The thermostat is one for sure and is unique to the 351 C engine. Search the forum some recent posts on the subject. Here are some other items you should check.
Is radiator cap good and proper pressure?
Are the radiator hoses in good shape not collapsing?
Is there a good flow of water through the radiator?
Is there signs of build up of corrosion on the ends of the radiator core when you look into the radiator?
When those all look good if you still have an issue have your system checked for a blow head gasket. You can do or have someone do it they put some special chemicals in container and put on the radiator. The color will change if there is exhaust gases getting into the cooling system.
You can remove your thermostat and put in pot of water and heat up to see if it is opening. If it is and is the correct style then you can reuse it. When you take the thermostat out clean the bolts and apply some anti seize to the threads to prevent locking up.
Here is a picture of one of the correct thermostats for the Cleveland engine. There are several different brands and member just posted great list a couple weeks ago giving all brands and the part numbers. The Cleveland thermostat has to have a feature that goes down into the baffle installed in the block. You can see it just below the thermostat when you pull it. If not there I would get one and install. I would use a 192 deg. thermostat. You would think a cooler one would make the engine stay cooler but not always true. If the thermostat is open too much, might be reason for overheat now, the water circulates too fast and does not have time to cool in the radiator.
Also when you put coolant in and mix with water use distilled water to keep any minerals out of the system.
I also drill a small hole in the thermostat to allow the air to escape when filling the system that way it does not have to burp when filling it. Maybe 1/32" dia. in an area outside of where it functions.
I recently found the ones in the pics at an old parts house that had been closed for years. Just do some looking in your area you will be surprised what might turn up.
Let us know what you find.
David