You don't know what the issue is until you investigate. I've never personally seen ignition timing overwhelm a liquid cooling system that was working properly. Too much advance will cause pings and knocks, but the ECU should sense them and make adjustments. If the ignition module prevents that, you'd hear pings and knocks inside your motor.
Confirm there isn't a problem with the cooling system before trying to diagnose by parts-swapping.
You spark plugs will tell you if combustion chamber temps are too hot. It is 100% free to look at them.
But don't take my word for it, I don't work on bikes or anything.