[Lynn Eades]

I'd suggest you run them, along with a full set of shrouds.
(BTW.I have not yet owned a carrier that runs) The thermostat is there to make the engine run at an even temperature. The higher the operating temp. without boiling, the more efficient the engine is. It is however imperative that the engine never boils. Thermostats will considerably lengthen the working life of the engine by reducing wear. Wear occurs because components are not at the correct sizes for a proper working relationship (due to running too cold and being too loose a fit)
Henry Ford never designed his first V8s to run thermostats, but he did move over to them. I believe the first ones were installed in the top radiator necks.
There is a lot of conjecture about thermostats in flathead v8s.
Thermostats will not (can not) keep the temp down, only raise and regulate the temperature.
Everything has to be in good order. Many times thermostats get the blame and are thrown out because an engine is over heating. The reality being that the radiator is clogged with gunk, the timing is out, the block is full of sand and rust, the engine is running lean, there are cylinders that are lazy, etc. etc. etc.
I have seen carriers that consistently overheat and when you take a look, half the shrouds are missing.
They have a big fan, which is noisy and can easy fail (fall.....or fly to bits!) usually wrecking the radiator. This fan has to draw air through a lot of restrictions and stuff it out the back some where. If bits are missing the air just "washes" around the blades, and the machine overheats.

The conclusion I have drawn is that the flathead v8 should run the lower temperature option of thermostat (173*F) as opposed to the higher (182*F) type. (my opinion)
There are many who think that modern thermostats don't flow enough. I have trouble with this as the V8 is fundamentally two small 4 cylinder engines, where the coolant only ever mixes in the radiator. Each of these two 4 cylinder engines runs its own thermostat. Many bigger, higher output engines only run one stat.
If however you have a problem here, then high flow stats are available.
I cannot recall, the exact model, but I recall that a late model Nissan thermostat is the right od, temp range to fit in the hose on top of the heads.
What used to happen was that people cut the older ones down, but the Japanese have further reduced the od of stats to a more convienient size (for us)
Just a point of interest, one side of a flathead v8 runs hotter than the other side (known fact)
Try a heat gun on the head outlets? It is due to different compression ratios and other design differences(one side to the other, of the same block)
More points of interest:
Carriers all came with pressure caps. Riveted carrier caps are adjustable (about 3 lb??)
In Nigels book, the radiators were up graded because they split the seams.
Aust carriers came with an adjustable valve in the overflow tube,but later went to a standard comercial 4 lb cap??
One pound of pressure (held in system) raises the boiling point by 4 degrees F at sea level, so a 4lb cap raises the boiling point, by 16*, from 212*F to 228*F. This allows a higher operating temp, kept up there with a thermostat, giving greater efficiency from the engine.