I spent some years as a mold maker for the injection molding biz. My molding room manager had a trick for increasing the cooling rate and shortening the time to cycle a mold. He'd turn the outlet valve down, closing the flow some forcing the water to say in the mold longer & cooling the mold more effectively. This (he contended) let the water (a phase change material) absorb more heat energy faster, because as he said water being a phase change material has a variable ability to take up energy. this ability changes dramatically as it takes on energy andchanged temperature. There are thermal regiems during which it takes up energy slowly and others where it does so rapidly. His contention was that if he kept the water in the mod just a wee skosh (pardon the highly technical terms) longer, it'd take up a lot more thermal energy and cool the mold more rapidly.
He was correct. the molds cooled faster and that let him run faster cycle times.
SOOOOOOOOOOO Logically allowing the coolant to stay in the heat exchanger a little longer will cause an uptick in energy transfer, improving cooling capacity for the benefit of the engine.
I was swinging at a diagnostic test. I will confess I don't have an advanced degree in thermodynamics.
Of no use to the OP and just for fun:
In a closed system, moving heat from point a (the block) to point b (the atmosphere).
Fluid that spends more time at point a will take on more heat load, up to the point it changes state (boils and turns to steam), at that point the coolant can take no more heat, and will fail at moving heat from a to b.
Fluid that spends more time exposed to point b will dump more heat. Right down to the point where it reaches ~ambient temperature, at that point it will release no more heat.
Both of the above statements are true, as is the following.........
Fluid flowing more rapidly from point a to point b will pick up less heat per given volume of fluid that if it was flowing at a slower rate. However, the fluid per time unit will move an equal amount of heat from point a to point b, it will just have a lower temperature differential than fluid with a restriction (thermostat).
Sincerely, anecdotal oddities aside, the reason you shouldn't run your ice without a thermostat for a long period of time; the engine will not consistently reach operating temperature, and will not perform at optimal power/fuel efficiency.
Now, this is a hoot, and ****, maybe I am wrong, but I was trying to get closer to a diagnosis for the OP, not telling her to run the tractor without a thermostat for hours unattended.
I don't think I am making a frustrating problem any easier to find. So for heaven sake, don't even consider staring your engine without a thermostat, for even a minute. The heat of the flames will exceed the early hydrogen bombs, children and baby seals will die, we must think of the children (and the seals)
Sorry for the side track op, it was with good intentions, please do let us know what you find.
Best,
ed