Actually the TEC/peltier in the seebeck configuration
is not used as a temperature sensor for LPMs.
It is used as a differential voltage sensor between the
front and rear plate's differential temperatures.
Well, it essentially is, at least when it measures the difference in temperature across a known thermal resistance, very similar how you would use a voltmeter with a shunt of known electrical resistance to measure current.
The problem is mostly that 'known thermal resistance' which you cannot purchase like a know electrical resistor you can use as a shunt to measure current by looking at the voltage across it.