Cant see it being thermostat as if its ok on idling for like you say an hour and not overheating then going for a ride should be ok.The fan on my bike kicks in after about 10-15mins on idle revs 1250rpm.
Lean mixture (check plugs should be a tan or grey colour) any thing that looks white ,means its running lean that will cause overheating ,have you got standard air cleaner in and are the carbs balanced?
Its also been friggin hot weather over a few days and if the engine is rebuilt it would get really hot with it being a tight engine.
