Thanks for all the good ideas!
I tried a original Huawei HB5N1H battery and can confirm that it worked. The original battery at least has a NTC103 type as thermistor between the middle terminal and the minus-terminal.
It went through the whole load-cycle without problems, temperature reading varied up to 36°C.
At room temperature the readings were slightly different, but NTCs are notoriously inaccurate.
Rumours have it that cheap 3rd-party batteries might have a constant 10kOhms resistor instead, which might lead to the battery catching fire, explode, you name it.
In case you want to use any replacement battery I would recommend to check that a NTC103 is installed. This can easily be done with a Ohm-Meter. The resistance between the middle terminal should be around 10kOhm at room temperature and the drop quickly if you warm-up the battery mildly (warm with your hand, place it in the sun or on some warm, not hot, surface).
I hope it doesn’t have to be mentioned here that using a lighter or other open flames are not a good idea.
If the resistance doesn’t significantly drop, don’t use it!
Hope this helps!