Is the fan cycling on and off when the needle is about halfway ??, i.e. 9 o'clock
....it should. If it isn't, then you have short in the thermal switch on the radiator.
If you're overheating at idle, standing still, I would think about first, draining and changing the coolant. I just did mine, and it's a requirement every two years. Remember to lean the bike left and right while burping the radiator (Cap Off). Do this several times to make sure an abundance of coolant is displacing all the air possible. Manual then says start and warm fully, let cool, check, and repeat several times to be sure. That is, warm up, cool down, check resevoir, repeat. After the second warm up cycle, cool down, I was good. No changes in coolant level. No issues at the needle as well.
A faulty radiator cap would allow an abundance of fluid and pressure out the cap, into the resevoir. Also causing an overheating condition. The system needs to build up pressure to stabilize the engine temp. If there's no pressure equilibrium there's going to be overheating.
Also, put the thermostat back in. It's designed around a warm up cycle mapping, and the coolant temp sensor relies on information, water temp, that the thermostat stabilizes. When warm it opens, and the coolant temp takes over from there, the fuel injection adjusts to it.
So replace with new thermostat, couldn't hurt, change radiator cap, couldn't hurt, and flush and replace coolant. Check all hoses clamps are tight prior to refilling. Once this was done, I would attach my stant pressure tester, just to make sure you have no bleeding of pressure. Either way, at this point, the cooling system is as it should be. Then check that the fan is cycling on and off when fully warmed up. Needle will be at 9 o'clock. If it isn't, get it working. That little radiator relies on the fan to help control the engine temp when the bike is standing still.
If all of these are taken care of, and operational, then you should be in good shape. If everything is as detailed, and you're STILL overheating, THEN I would take a compression test, and cooling system pressure test to discern if you have a leaking head gasket. I doubt it, unless it was accidentally run dry, and not properly refilled in an expedient time frame.
Repost after all is investigated. You'll find the culprit.
Funky gauge reactions are common from time to time, but true overheating is not a problematic Hayabusa issue.
Figure it out, and get back out there and RIDE !!!!