When the TMP01 is powered up, what is the timing of the UNDERb and OVERb pins? Before they settle, are they random or are they pulled high/low?
The UNDERb and OVERb pins are open collector outputs. The output settling time depends on the value of pull-up resistors used. A strong pull-up (Low value resistor) will give a faster power-on settling time but this also causes alot of current to be sunk by the part which could cause self-heating in the device. A pull-up resistor in the range 4k7 to 10k is recommended on each UNDERb and OVERb output pin.