Sue, how hot does it get up there in Ontario, Canada anyhow?
You are correct about raising mowing height. That way the grass can shade itself.
I never mow less than 4".
I live in Florida and NEVER water my St Augustine lawn or even my Bahia grass lawn.
I also have trees that provide shade at various times of the day. And that helps keep the yard cooled off.
Most of my daylilies get afternoon shade, and I notice many have set pods they wouldn't do if too hot.