I went through this issue as I have the 261 thermostat. Yes, closing the heater valve may be an problem if it shuts off the bypass. I have a tee plumbed into the heater hose so the bypass works in any case. There has been a lot of discussion about this in the past. e.g.

https://www.stovebolt.com/ubbthreads/ubbthreads.php/topics/1445405/all/261-bypass-thermostat.html

Gord 🇨🇦
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1954 1/2 ton 235 4 speed