I trained and road raced shirtless almost year around for 36 years in Miami. Coached high school kids - and ran with them in practice - and we never wore shirts. They did, of course, for meets.
Before road races - which were always 10K or longer back then - I took an empty half gallon milk jug, filled it with cold water, and poured it over my head just before the start. Pretty sight? No! But if I didn't do it I would be a hot, wet, sweaty mess a lot sooner, so my goal was to put it off as long as possible.
Before Cross Country meets my kids would pour cups of cold water over their heads, to at least start out cool. Other teams saw us do it. I mentioned it sometimes at coaching clinics. My kids won the Miami Dade County Youth Fair Championships (the defacto County championships back then) five out of six years and won State 5 times between 1982 and 1997. And I never saw any other team give "watering down" - as we called it - a try. Though at State in 1988, on a brutally hot day in St. Petersburg, the #1 ranked kid, on another team. asked if he could have some cold water and my kids let him. And he won. Which, yeah, he might well have done anyway. 😀
It seemed so obvious, but only in recent years have cool vests become available. A wee bit more classy than cups of ice water and my own half gallon-over-my-head tactic.