I've never found cooling to be necessary for breeding myself, although it could be a way of triggering "out of season" mating.as long as previously cooled
I've had eggs laid in November, so late breeding is perfectly possible. As long as you can source food for hatchlings outside of the normal breeding season, there's no reason why you shouldn't give it a try.
As Cornflake saiys, they'll either get to it or they won't and you won't know until you try!
I had no idea this was possible!