Battery Temp Sensor On Early 2011 MacBook Pro

I need help, I am restoring this lovely Early 2011 MacBook Pro 13inch And it has started developing a problem, When running on battery power sometimes the machine just shuts of like the battery has been pulled. I have run Apples Hardware Test and sometimes got this error code - 4SNS/1/T0000008:TBOT--124.

I Have got it down to this being a Temperature sensor but i am very confused as the shutdowns seem to be totally random and that after running the Diagnostics multiple times with the charger connected and also disconnected the error does not seem to appear most of the time. Can someone please help me as i don't want this beautiful MacBook to go. Is there any way to fix it as apple can't repair it anymore, and will just replacing the battery fix the issue as it is a battery sensor that is faulty. Please give me all the information you have on this issue and anything i can do / try. Thank you.