MacBook Pro shutdown at the slightest temperature increase

I have a mid 2012 15” MacBook Pro with Retina display.

My computer only works in cold temperatures. For example, after shutting down, I tried turning it back on, but it wouldn’t work, until I took it outside to cool down in sub-0 temperatures. It would turn on again until it starts heating up slowly.

When the laptop is turned on, the temperature usually starts at 29 degrees Celsius. At about 30 - 31, the laptop shuts down. I tested this and found that if I wasn’t opening a lot of programs, it would last a good period of time, compared to if I opened several programs.

Other issues include the battery, which needs replacement (over 1200 cycles). The laptop doesn’t turn on without being plugged in, but I figured that’s not the issue if it’s charging.

A preliminary troubleshoot was done at Apple - the fans and everything else is working fine, except the logic board. Couldn’t finish testing the logic board because the laptop shut down. Apple suspects it’s an issue with the logic board and told me I’d need to replace it along with the battery in the hopes it gets fixed. About $1000 cost. He recommends I buy a new laptop.

Hoping there’s a fix for this. Please let me know your thoughts!