I'm a bit confused as to why these people don't have water. If they're working in fields, then those fields require water, so there must be some reasonably close by. Granted, we can find some cases where people do hard work in places that lack nearby water supplies, but those exist today as well. People bring water bottles. I doubt you'll find many cases where humans worked in hot, waterless environments without having some means of bringing in water. I doubt it for the simple reason that it is impossible to do without dying of heat exhaustion, as you pointed out in your question.

My expertise only covers Egypt, but I think it's a good case study, because most people think of Egypt as being very very dry. I can't be totally sure, but I believe that this misconception is the result of Hollywood. Movies about Egypt spend most of their time in desert settings, but Egypt doesn't really look like this, it looks like this.^1 Ancient Egyptians only lived in the lush environment of the Nile Valley and Delta, where water and shade are abundant. If you were working in a field, that field was irrigated by a canal dug from the river, meaning that there was water all around all the time. Some of that water was not always good to drink, but they made beer and wine for precisely that reason.^2

Egyptian houses were built of adobe^3, sunbaked mudbrick with a dried mud or plaster coating. Adobe buildings are well insulated against heat, especially when covered in a reflective outer surface. I can tell you from personal experience that these buildings are actually pretty comfortable, even on hot days. Egyptian buildings also included specific features designed to reduce the interior temperature, including latticed windows high in the walls that let light in and hot air out (as seen in this model of a temple from Penn Museum) and courtyards with pools (as seen in this model from the Met). They knew how to get out of the heat when they wanted to.

There's even an Egyptian word (𓈎𓃀𓎛𓅱𓏁𓈗 or similar) that means variously "coolness", "cold water", or "refreshment", and it is connected to offerings of "cool water" that were made to the gods and the deceased. They understood well the connection between water and coolness and valued it to the point of holiness. Numerous texts celebrate the relaxing and cooling powers of water. The Egyptians certainly understood that you would need water if you were out working in the fields on a hot day. They brought water.

Notes

1. This trope annoys me so much that I started writing a historical fantasy novel set in Egypt where almost none of it takes place in the desert, just so there would be some story out there that doesn't do the whole "everything is desert" thing. I haven't finished it yet, but if you're interested, read the draft of the first chapter and tell me what you think so far.
2. If you're thinking: "Wasn't everybody drunk?", the answer is: "Yeah, a little". Cooney's The Woman Who Would Be King paints an excellent picture of court life in a world where everyone was slightly buzzed at all times. (Addendum: People also drank water from water purification and storage devices, such as wells and cisterns. See u/PalmamQuiMeruitFerat's comment below and my reply to it for more.)
3. Fun fact, the word "adobe" originally comes from the ancient Egyptian word for brick. It goes: Egyptian 𓂧𓃀𓏏𓊌 → Coptic ⲧⲱⲱⲃⲉ → Arabic الطوبة → Spanish adobe → English.

Edits

1. Added the "Notes" heading because the notes and text were too close and it didn't look nice.
2. Fixed a broken link.
3. Added the addendum about drinking water to note 2.

I can’t answer the question but here’s one that is specific to native Americans by /u/theadjunctprof, there is also another similar question linked in the comments.

https://www.reddit.com/r/AskHistorians/comments/hl34hl/how_did_native_americans_handle_the_heat_of_the/?utm_source=share&utm_medium=ios_app&utm_name=iossmf

Here is another answer, also about the south west.

By AlotOfReading or /u/alotofreading as the auto-moderator wants

https://www.reddit.com/r/AskHistorians/comments/c8rizq/how_did_native_americans_in_the_american/

Here is a cool picture they link of adobe houses.

https://chambersarchitects.com/wp-content/uploads/2016/09/Taos_Pueblo_Wikimedia_Commons_Luca_Galuzzi.jpg

This my favourite sub ever. Thoughtful and insightful answers to some really good offbeat questions. You guys rock my day, thank you from the bottom of my quarantined heart.

Thanks for the depth of that answer! This is why I read comments