IPhone 8 Powering Down

Have an iPhone 8, and one day it just wouldn't turn on. Tested chargers, outlets, did all the things the internet vids told me. Make an appintment with a local phone fixer upper company, put the phone in my vehicle the night before to be sure not to forget it (my kids phone). It was a chillier night, got into the low 40's. When i get in my vehicle, i pick the phone up to move it and waalaaah, it turns on. I explain this to the phone fixer upper folks and they test it, run diagnostics and can't tell that anything is wrong. Anyway, I go back and pick it up, and righ there, when he hands the phone to me, it resets itselfs unprovoked. I take it anyway and the phone does it again, only this time, I stick it in the fridge for 10 minutes and it turns on. Take it back, they do whatever they do and they say it's the battery - i buy a new battery and they install. Surprising, this wasn't the fix. Does anyone know why it will just turn off but will turn back on if cooled? My daughter literally just played on it for several hours and nothing happened. It's so random, but coolling it off remedies the issue. Anyone have an idea?