I have to side with Bruce, & Toolman on this one. The engine should run cooler with the thermostat removed providing the rest of the cooling system is functional. The only purpose for a theromstat is to allow engine to achieve operating temperature asap and maintain it there for maximum efficiency by modulating the flow. This results in max power output & effiency, longer engine life, etc.
I have worked on hundreds upon hundreds of gas & diesel engines of road design, stationary units as well as marine design and although their cooling sysems may differ they all do the same thing. A tractor is much easier in design.
BTW, the main purpose of the bypass hose system is to permit coolant flow between the block and the suction side of the water pump when the thermostat is closed to provide uniform warming of the block during warm-up. True there are some that may circulate it thru a heater core then the radiator as the bypass but that is only primarilly for the passenger heat.
In my opine removing the thermostat will make the engine run cooler assuming all systems are working properly.
I believe the poster having the overheating concern has a problem in another area. Some areas of concern: clogged radiator fins(maybe internal passages), block/head cooling passages sludged up, defective water pump as in impeller bad or belt slipping. Hose collapsing(lower radiator hose)Head gasket leaking some combustion gases into coolant, radiator cap, intake or exhaust restriction, timing, airflow over radiator. These are just some areas that I thought of quickly at the moment and there may be others. Always check the easy first I always say.
I would first suggest to the poster to verify with a known temp gauge what the temp really is.