I would think it's the sprag too. The starter is possibly in need of replacement also. It's hard to diagnose a video.
IMO....given the mileage and if it does turn out to be the sprag, I would replace the sprag and ALL related parts-bushings, starter gear, etc. I recently had my sprag replaced at FBF. They won't "just" replace the sprag anymore on the 999 models. There's too much wear on other associated parts which could cause issue's by just fitting a new sprag. It's not a great idea mixing old worn and new parts. There's two problem area's with the 999-one the right side main bearing, two, the sprag unit-it;s very, very weak.
It's sounds too far gone to trim or fit a new spring.
IMO the answer to your question is NO. A colder engine would exacerbate a bad sprag. A hotter engine would turn over easier making it easier on the sprag. Curious how others feel.
Let us know how you make out....