Phone keeps turning off unless kept cold. What could be the problem?

Hello! My blackberry key2 Recently started to have issues randomly shutting off. Getting to the point where it was effectively boot looping, with random time periods of clarity where it could be used shortly.

Was still occurring in safe mode, but overall the issue was sporatic and sometimes I could get like 5-10 mins of use out of it. I tried on the charger, full charge, etc with no luck or changes.

Out of desperation I put my phone in the fridge, and found out that it worked fine without any issues when it was kept cold.

I assumed that meant it was for sure a bad battery, so I ordered and just replaced the battery last night. The problem still persists exactly the same.

I found I can continue to use my phone by simply keeping it on an ice pack without any issues...

Also I am pretty confident it is not overheating. It would often get warnings about heat or w/e that it is not doing, and it does not feel hot or warm to the touch even when rebooting (although its possible an individual small part is still overheating). Also the weather is not currently warm, and when the phone is on the ice pack its not kept that cold tbh.

Does anyone have any ideas what the issue would be and how to troubleshoot/fix such an issue?

Thanks!