Warm-up vs CoolDown and their impact on the Auto Scaling Group

I went through AWS documentation on those two concepts (Warm-up and Cooldown) but I found that there is some overlap. And I haven’t found yet a documentation explaining how the Auto Scaling Group is taking into account those two factors. Can someone here please explain what is the relationship between those two factors? 

Especially what will be the behavior of the ASG if the warm-up period is greater than the cooldown period?