“Regarding the battery it’s probably because i was forced to buy the physical sim version here in Europe

yet another downside thanks to the EU when it comes to Apple this year

..”
I don’t think it makes that much of a difference. I was a little worried about this as well, but then I thought a bit more about it and realized it differs only two hours (in terms of watching video) between the physical SIM and eSIM only models. Two hours sounds like a lot, but when you compare directly to the iPhone 15 Pro Max you’re still getting 8 extra hours out of it rather than 10. Yes, of course 10 would’ve been even better, and I believe there should have been an option to get eSIM only as well (especially since you can after all get the iPhone Air, which is globally eSIM only). But any + in battery life nice.
That said, if you’re experiencing issues with battery life it’s usually either a defective battery (meaning you should have Apple fix it) or you could try and change some settings. The latter might not sound ideal - you bought an expensive smartphone and don’t want to have to turn down a slate of settings to make it work right for you - but sometimes there’s options you clearly don’t need nor use. Disabling those might help at least a bit. Think of turning off background updating of apps, turning off notifications for apps you don’t need notifications from, that sort of stuff.
As for heat: I haven’t experienced such thing yet, although I should add I don’t play any games other than Duolingo and Wordfeud. Mostly it’s just WhatsApp, browsing the web, using e-mail, making calls, watching videos, scrolling through Facebook/Instagram and shooting photos and videos.