Given that you're from the UK, and temps are usually cool, you shouldn't have overheating issues. Also, as soon as you click second gear, you'll have a decent amount of air moving over the rads. As others have said, stop and go traffic could be where you have problems, although I doubt it.
Unfortunately I don't have any experience with a 300EXC motard, to know for sure. I would just take it for a run and see how it goes.
I'd think your biggest concern is getting the jetting rich enough so that it's sufficiently lubricated, but not blubbering in traffic. Fuel supply is actually one of the main ways a 2-stroke is cooled, and not enough fuel can lead to overheating and seizing, most likely at half to wide open throttle.
Other non-mx forums (like thumpertalk) or a local ktm shop might have more specifics for you.
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