I breed year round, they go when they wanna go.
I have a girl that will be laying eggs in the begining of October, she obviuosly bred during the warmer months.
I have another girl who laid in Feb.

This year I didnt cool and got the same exact results of last year when I cooled. Of course the weather change naturally cools, even here in southern cali.

Answer to your question there is nothing wrong with trying before cooling season, actually the sexual activity can help the female begin her cycle so go for it. You got nothing to loose