Heat waves are basically the only serious thing here. There isn't really much to surviving them for the average person. Stay where it's cool, stay hydrated, don't over exert yourself in the heat. All really easy things to do if you have a reasonable amount of security in your life. Most don't bother except maybe making sure to contact elderly or otherwise vulnerable relatives.

Preparation is needed if you're not financially secure. Maybe you're homeless, maybe you're too broke too cool your home, maybe a lot of things. I've been there before. To this day I'm still aware of places I can find shelter across the city and how to get to them, with and without public transport, in a hurry.

Mostly the answer is libraries but it depends where you are in the sprawl and how bad the heat wave is. They're great during business hours but they can close before things cool down. I learned to get really good at loitering in shops and other private places while expending as little as possible without them moving me on.

Also where to get potable drinking water for free, you'll be surprised how hard it can be to find in a pinch.

Edit: I forgot an underrated and personal favorite method from those days - trains.

Before everything went electronic it was really easy to travel free without the stereotypical methods of fair evading, so you could relax when inspectors were on. I'd find a train with functioning air conditioning on one of the 'safe' lines and just ride it for the whole round trip back to the central station then find a new one. Outside of peak hour it would be dead quiet and I could read or sleep in peace, and they go till late.

If you're curious about the fair evasion method, the old tickets were just small bits of plastic-y cardboard with a magnetic strip on the back. Ticket machines would read the magnetic strip, write to it and mark down a trip in ink on the front of the ticket. If the magnetic strip ever failed they'd still honor the ticket and use the marks on the front to determine how many trips you were owed.

All you had to do was stop it being inked (or remove it). The tolerances on the machines were quite large so you could easily just put a bit of tape on the front and peel it off after to have an unmarked ticket. If you were desperate, you could sometimes rub it off anyway. Then all you needed to do was run a magnet over the magnetic strip or bend the ticket until it was damaged in the right way for a "fresh" but broken ticket. You'd then exchange it as a broken one and have a new ticket. If inspectors ever came around while you had a broken one they'd just tell you to take it in and leave you be.

This way you'd theoretically only ever need to buy one ticket, though it was still advisable to pay when you could or fair evade other ways to avoid become a regular at the service stand. My mother was an alcoholic and my father a deadbeat so this was how I made it to school for years.

I'm sure there is some trick with the new electronic cards but I've been fortunate enough to not need to work that out since they came in.