Computer shutsdown under heavy load after reaching 45ºC

I recently replaced my old battery to a new A1494 one from ifixit but the computer started doing some weird shutdowns.

At the beginning I tried re-calibrating and I have done it twice. Full charge and then wait ~6h and full discharge and wait overnight (I know it is supposed to be +2h, but at this point I rather make sure it did calibrate). This didn't solve the issue so I then did a PRAM reset followed by an SMC one. Didn't work either.

Then I started realizing that the computer would shutdown under heavy loads (~80W, I just let a program running in a loop, turn the fans to the maximum and run a video on youtube) and reaching 45ºC and then shutdown because of it. Here's a screenshot:

This problem doesnt happen with the old battery. It doesnt even reach the >45ºC under the same load.

Anyways, I already asked ifixit for a replacement battery, but I'm afraid it doesnt work as I saw a thread where the guy replaced the battery 3 times and it didn't solve the issue until he went to an official apple store to make the replacement.

Do you guys ever experienced something similar and were able to fix it? The computer is almost 10 years old and never stopped working properly, I just wanted to replace the battery to make it last longer as the current one ist at 50% of the design capacity.

Thank you!