And if it's not cool enough, release the starter switch, let it coast down, and if necessary hit it again. I've never needed to use more than two cycles. If I need to cool it down, I press the starter and motor it to maybe 10%, quit, and the second time it's always below 150 before reaching 15%. You don't want to use any more battery power than necessary.

If you just press the starter for a few seconds to cool down the TOT, does it record a start cycle?

3 pages on starting the engine!
Good grief.

Motoring the engine with no fuel introduced does not constitute a cycle. I've never flown a 206 that recorded cycles, it has always been done by the pilot keeping track.