You say it gets so cold its stops running correctly, that sounds a bit strange tbh as it obviously starts up ok from cold. It's not the carb icing up is it? Do you still have the std air filter that has a feed from above the exhaust?
it does have a k&n on it and the hot feed is removed so i think once it gets so cold it does ice up, but this shouldn't make it go cold well imo, i could be wrong but it's not running cool the plug's have a nice grey/brown colour to them so should still be producing enough heat just to keep the jacket warm,