I've had audience members suffer from heatstroke when working in outdoor theater - but that didn't stop the show. In 6 years of outdoor Shakespeare, I haven't experienced calling a show because of heat.
We've always had modified plans for blocking (no sitting on the hot deck), costumes (removing certain pieces, adding ice vests under shirts) and bare feet (having an alternative). And tons of water stations & ice backstage/in the wings.
There is a lot to consider regarding weather when outdoors - rain, heat, cold, wind, wild animals. The company I worked for had a general rain policy (based on how high the rain bounced off the deck) but didn't have the other policies. These would tend to get worked out on a case by case basis. Talk with your deputy and always check the weather in advance. If it looks like it's going to get hot in the coming days, pull people in for a discussion to try to plan ahead.
I will say, working with AGMA ballet dancers, our contract (which was company-specific) had rules regarding minimum and maximum temperatures. Unfortunately the contract contradicted itself, one time saying I (as the SM) would decide if the show would go on if the temp exceeded the contract max, as long as we paid a fee to the dancers. Another part said that AGMA had to approve whether or not the show went on. Thankfully we never hit that limit - we got close in the studios one year, but never exceeded the limit.
However, we did get below our minimum temperature while on tour. It was winter in Spain and the windows in the theater were broken. We couldn't fix the windows (they were already covered with cardboard and tape) and no matter how many translators I went through to explain that we had to get the stage above 23*C, the theater wouldn't budge. And we weren't allowed to cancel the show. And no, I don't think my dancers ever got paid for that break of the contract.