So, 2 of my phones had their batteries expand after crunching WUs with a 40C max temp.
The temperature really depends on how far the battery is from the CPU, and if the CPU cools via the screen and back panel, or only the screen (and have a plastic back plate).

On my Samsung Galaxy phones, I've lowered my max temp to 38C, but it still feels quite hot; so I personally would recommend anyone who is crunching data on their phones, to set 37C as the max battery temperature to crunch data on. 35C being a lot safer of a margin.
If your phone is in a colder environment, you could go a degree or two higher on the temps, but anyone who has their phones in an ambient temperature of 70F or higher, should preferably keep the battery temperature below 37C; 35C if you're in 80-85F ambient, and ~30C if ambient temperatures exceed 90F, or the phone is in direct sunlight (not recommended).

Not had a battery expand yet but my now retired FP2 would get very hot, either when crunching or using it as a satnav and would stop charging. Using it as a satnav became impossible as it would produce random reboots, much more common when hot though occasionally at other times too. FP3 doesn't seem to heat up at all used as satnav and runs cool when only using one core. I may up it to two cores and keep a close eye on it to see what happens. I have BOINC set to stop processing at 36C as I use it as my main phone and can't afford to have it go belly up.

I bought a Samsung Galaxy A71 with the specific purpose that it could do 6 threads at a time.
Unfortunately, after a Boinc and system update, I can now only do 4 threads, and even then it overheats (regularly has to throttle down).

I have 2 Android phones that BOINC:
Samsung A01, 8 "core";
Motorola G6, 8 "core";

Both can only use 3 of 8 to crunch w/o overheating and/or random shutdown at 37 & 39 C respectively.

Had to replace battery in the Motorola after using the GPS/GOOGLE MAPS on a trip for about 4 hours due to swelling and overheating.

Seems the phones and their batteries nowadays are not designed to be "worked hard" for a extended period of time.

As ever, with computing components, the best course of action to take to cool things down is a moving air stream across the surface of the computing device. You don't just jot a multi-core CPU in your case without cooling it with a fan either, do you? So just place a fan next to your Android devices that blows its air over the front or back of the devices and it'll cool your device down. A small USB powered desk fan will do. It's cheaper than replacing the battery every 3 months.