You could survive nearly any extreme heat/ wet bulb event without power with under $500 worth of equipment…

With a couple hundred watts of solar panels ($200), a modest sized power bank/solar “generator”($250), and a cheap table top ice machine ($60-100). This assumes of course that it will be sunny, but given we are talking about extreme heat that’s a reasonable assumption. You could also run it off a car inverter or a generator, if you have fuel. You could make ice during the day and store it in a cooler for nights. Bagged ice in armpits/groin, ice baths, etc.

Also cold drinks!