never heard of one 'designed to stay open' when the water isn't hot or "just in case" - thermostats open as the water heats up, close as the water cools down - unless the 'design' was on your part and you wedged it open .... a stuck open stat can allow the coolant to move thru too fast and not take away enough heat .... and a gauge that reads cold when the rad is too hot to touch is defective, even if the sensor tube is OK
you need to get a laser thermometer and check various points on the engine and rad to see what's really going on, your first description sounds like a temperature problem, you can't run these old bolts around for an hour and have them still be 'cold', and if it wouldn't crank well until it sat for an hour it was too hot
Bill