Broccoli should send out small side shoots, one on each sucker, for a while. Different varieties give different amounts but over time I often get more broccoli from side shoots than the main head. I do not notice that much of a difference in taste but maybe you will. Eventually they shut down in the heat or they get so buggy you will not want to eat them, but I keep these going as long as I can.
Kale does taste better in cooler weather, it can get strong in warmer weather. But again it will keep growing until it does turn really hot as long as you keep it cut back. I usually keep kale going until it becomes so buggy I don't want to eat it. The problem for me is those little green cabbage worms.
Lettuce will turn bitter and bolt when it warms up. Go by taste instead of the calendar but this will soon be done.
Spinach is one I never had luck with, I quit planting it because the productivity was so bad even in a "good" year. It was heat sensitive, one of the first things to die when it warmed up. Again make your decision by what you are getting out of the garden but I don't think this one will remain a mystery very long.