Within a hundred yards of starting there would be no way to know the t-stat is bad, in my opinion, except perhaps for pins shorted to +12 or ground. There's no way temperature would build so quickly.
The pump, on the other hand, could detect 0 revolutions very quickly and pop a warning.
I used INPA on my E90 to test the water pump, fan and all kinds of stuff just for kicks. It is annoying that ISTA doesn't give pump rev feedback. I haven't tried to run INPA on the F10. If it works, it might be a better tool for this purpose. With INPA you could request a target water pump % and read back the resulting RPM if my memory is correct.
ALSO: for the pump you could try activation the bleed function. Turn on ignition, don't start engine, throttle pedal to the floor for 10s, if I remember correctly. You should hear it then, although if you are not accustomed to exactly how it sounds when everything is working properly it might not be a perfect tool.
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