Sorry thanks for the correction. Based on this "Monitor Beeper" test straight from the manual, I conclude the temp sensor is a on/off switch. So yes you could check it for continuity cold, then check it for continuity hot. I suspect you would need to put it in a pot of boiling water (no different than testing thermostats) with some jumpers to measure continuity.
Monitoring Beeper
If beeper does not emit diagnostic codes anymore,
while the MPEM gauge supply outlet
works, check if beeper functions well, as follows :
1. Access 33-second temporization mode.
2. Disconnect engine overheating sensor wire
(any wire on Speedster).
3. Ground the disconnected wire.
4. Beeper should be functional. Otherwise, check
wiring harness. Also check the beeper by supplying
an external 12 Vdc directly to its harness.
Polarity is mandatory. Connect the positive supply
wire to the PURPLE / TAN wire.