Q: Failed Thermal Sensor on MBP

There are about a dozen thermal sensors. Most of them are inside other parts such as the processor and Apple-certified RAM DIMMs. There are a few that may be on heatsinks and other seemingly random places. There is also an RPM output on each cooling fan.

A poor connection of a sensor cable can cause a sensor to read its minimum or maximum, and therefore out of range.

Your post is confusing.  If Apple replaced the battery and it won't run on that battery, then the battery upgrade is most certainly NOT "functioning properly"!  And nothing from what you post to me indicates anything at all wrong with a thermal sensor?

Did Apple actually do the battery replacement?  If so, take it back to them as that work and parts are warrantied for 90 days.  If you did it yourself or someone else did it for you, then you need to check the battery connections, and if not them, the battery itself.  In other words, if the machine runs fine when plugged in, but the minute you unplug the power supply it dies, then the problem is either with the battery itself, or the connections and installation of that battery.

Did Apple install the battery? If not, it is not a genuine Apple battery.

There are many thermal sensors--if damaged most require a new logic board. If you have the original disks that came with the computer, running Apple Hardware Test or Apple Diagnostics from those disks will usually identify which if any sensors are bad. If you  get an error code from the diagnostic test, post it here and we can make an attempt to translate it.

You can run System Information (SI) to read the battery serial number and other battery data. Invoke SI by either launching it from your Utilities folder, or doing "About this Mac" from the Apple menu and clicking "System Report" in the resulting window. When SI come up, select "Power from its left-hand pane to get this:

Look for your battery serial number--it's redacted with a red bar in the image. There are many counterfeit batteries out there because of Apple's decision to no longer sell replacement batteries as a service part directly to users. Many of the counterfeits have the same serial number--0123456789ABC. Serial numbers should be unique, not the same, and should not look like a password from a Mel Brooks comedy.

Also post the information I've outlined in red. It will show battery condition.

If you or someone other than Apple replaced the battery and damaged a sensor in the process, then the cost of a new logic board could be in your future.

well, you can guess whatever cause you want. I think you have a more serious problem if the battery is not working. When I have such issues, I do the Install procedure again, and try to find out why it might mot be working.

The last problem with a sensor reported here was fixed when the user re-seated his fan connector cable.

Thanks, but the battery IS working.

What you have is a known-good part (battery), and the way it is currently installed, or the current state of the battery in the computer where it is installed is "not working".

The symptoms you describe - a system that runs fine when plugged in but which immediately dies when unplugged is not at all a symptom of a bad thermal sensor, in my experience.  You can disable those, or run with them malfunctioning, on all sorts of computers and laptops.  They do not immediately cut the power to the system on any laptop just because the power source changes.  A bad thermal sensor will cause warnings, erratic fan behavior, and if the cpu or gpu temps exceed Intels limits, they can shut down the system, but those shutdowns will actually be in the system logs and they would occur regardless of power source.

All to say, I think you have something entirely different going on - a bad connection, damaged power management system on the logic board - something that still may require a logic board replacement, but not a thermal sensor issue.

Why don't you run an Apple Hardware Test.  If there are sensor issues, this should show them. Right now you are just guessing.

https://support.apple.com/en-us/HT201257

Note that an error free AHT is not conclusive.

Ciao.