Forgot to say, but phone was really really hot.

Latest iOS 16.3.1, brightness was about 20%, ambient temperature 24'C.

What is the purpose of this?

Well... If you gonna gaming for 2-3 hours, you can't because it will throttle hard. So performance would gone down and the results...

Not all games will stress the device as much as your test.

I’ve never had an issue on any of my iPhones, I can’t even get my display to dim automatically like everyone talks about when it warms up. I play intensive games like League Of Legends Wild Rift on 120fps and the highest quality it allows when running 120 which is one tick from the highest visual quality and it literally stays pinned at 120fps and it only gets slightly warm to the touch and never throttles down or has any lag spikes or buffers. I also play Skyrim Blades and that has no issues or throttling or dimming either and I always run my phone at 85-90% brightness as well 24/7 with no heating issues on my 13 pro max. Not sure if the spec bumps on the A16 with minimal cooling improvements is the reason for this result you got but benchmarks are also benchmarks.. those tests are not true to most iOS games with cpu and gpu loads on the processors. Games vary greatly and even games you’d think would run your cpu and gpu to the max don’t ever actually utilize the entire cpu or gpu. So benchmarks should be taken with a grain of salt truly.

I think maybe it's my unit. I tried DUNE https://apps.apple.com/us/app/dune/id1291851950 and just after a couple of minutes it gets crazy hot. This is not so graphicaly intense game, but it gets my device runs hot. Girlfriend playing for hours same game and maybe it is warm at best.