Nah.
It's all about adaptation.
Our plants rapidly acclimatize, and the leaves from about midway up to the top of the plant grow long johns to help them colour cure properly as fall sets in.
Seriously, all my leaf has been hung from the ceiling joists in tractor or machine storage sheds each fall/winter, and I've had very few green leaves as a result. Occasional mould along the midribs of the largest leaves, and one year a fair bit on the tips of some leaf.
No heat, no s**t!