Sounds like it's working but I'd be a little concerned that the by-pass is still open and, that much, fluid is not circulating through the radiator. In the pic. you can see the second valve for the by-pass.(Little disc on the right) ,
Also, before you order a rebuild kit, check the block for cracks around the liners. Pull them first, or have whoever you get to rebuild it check.
I just rebuilt mine because I couldn't keep it cool. I live at 7000 ft. which has a lot to do with it but when the head was pulled I found little cracks radiating away from #1 exhaust valve set. Fun. Seems that there were a lot of problems with the original head and they( Detroit) began specking the head for the turbo charged 353. Same, but much harder and tolerant of high temps.
Would love to turbo my Goat but that cast iron block will not bolt in.