If you are only having problmes after the refurbs, I'd look into that .....
I'm not sure what kind of emission controls, if any, are on those tractors but running without a t/stat in our cars would mean extended warm up times and higher emissions, lower mileage.
You might just have a restricted flow thru the new rads which is causing the overheating. All else being good, running without a t/stat wont cause you to overheat.