Hello,
I just wanted to add my experience feedback. I had the same issue : alert for low temperature. And later shutdown and unable to restart the xiaomi 9T pro : icon of crossed batterie with red low level.
I thought it was after a Miui app update.
I have to add to my comment that I changed the screen a month ago. I use it since, without having completely glued the back.
So it's easier to access during test period if ever I add an issue.
When I open again the back of the 9 TPRO to access to the battery, I was able to restart it and the battery level was indicated 25% where yesterday it was 3% before troubleshooting. Just opening the cover, was just surprising to have this effect.
12 minutes later, I was with 60% and again a temperature alert. It shut down again and again unable to restart it.
So I decided to just disconnect the battery to have a hardware reaction. When I unscrewed the 12 screws of the upper zone, I discovered that the battery has disconnected from its plug. But I'm sure I connected it well and firmly last time
So, after reconnecting the battery firmly, I was able to charge it again, and restarting it. And since this action, no more temperature alert.
Maybe, you could check that the battery is still well connected on your phone. But you will have to open it.
Smal advice : it's not sure that your problem is the same as mine. If you intend to open you phone, you need to heat it (not too much) for softening the glue. And need a very fine patula tool to open it (0.3mm is not fine enough; 0.2 or 0.15mm is better).
It's not complicated, but if you want to do it without scratchs, buy some special tools. Fine spatula should be in metal. But later, work with plastic tools. It avoids scratch aspects.
Best regards.
Pierre B.