When I run flatheads I took the center flap out of thermostat and used the thermo housing for a restriction to slow coolant flow . Had no trouble with warm up or overheating.
Depends on whether you drive in colder weather or not. I don't run any in mine but then I don't drive it in winter. Slowing coolant down is an old wives tale. It's all about having a clean radiator and block.
No, they heat up just fine without them. I have tried both with and without and not had significant difference. Also read many threads on the subject with opinions both ways, I think it best to see what your individual car likes best.
The precise answer is: maybe. It will depend on your build, state-of-tune, driving style, elevation, and climate. I always put them in, and rarely take them out. You are going to have to try for yourself.
I have had flatheads for 53 years; never ran a thermostat EVER! Most of the time I would have a washer in the hoses with a 5/8-3/4 in opening; seemed to work well summer or winter. I spend a lot of time with a "hook" apparatus to dig out all the sand and crud that is left after the block comes back from the machine shop.I finish up by "tumbling the block" on a piece of 1/2 plywood.Did I mention that I have never had a fan on any of my flatheads,even ran a Deuce five window for 10 years with a S.C.o.T. Blower with a full hood in southeast Texas and no fan of any kind,mechanical or electric.Fans take 5-8 horsepower to run and flatheads are not known for horsepower output so why take an underpowered engine and cripple even more with a fan.Keep it moving and watch the temp gauge and you'll be fine.
No stats in mine either. I did the same as flatheadjohn and dug casting sand and then tumbled the block on plywood.
ANY engine driven on the street should have thermostat(s). Its only purpose is to allow the engine to reach operating temperature quickly, then maintain it. If you aren't doing that, you engine will run less efficiently until it can reach correct operating temp. Running under temp will increase fuel consumption, carbon build up and sludge formation. Unless you are building a race engine, put a thermostat in it.
Ford spent the first couple of years of flathead production debugging the beast...one of the early changes, I think in 1933, was the addition of thermostats. Most engines, including flatheads, will run cool when in use at low power levels like chugging around town. Anytime your engine is running too cool...let's pin that at 170-180...lots of bad stuff is happening. Oil is cold...so its flow isn't right since it is formulated to run at proper engine temp, AND water and nasty fumes are building up in the oil since it is too cold to cook them off. Sludge, acid... Engine clearances are all wrong...bearings, pistons, rings, etc. are all clearanced to run at a proper temp and everything is sloppy with blowby and extra wear happening. All those metal objects are meant to fit and run at a certain level of heat expansion, like about 180 for older engines. If your engine is running below 170-180 for any time except the first couple of minutes after fire up you have wear and lowered efficiency from a lot of different things going on. Not very many engines will maintain a high enough temp if cruising around town on a 60 or 70 degree day... Current stats do seem to have a considerable failure rate...at very least, boil the things on the stove and see if they open up a little before real boiling.