is there a way to bypass this to see if ts shutting off the alternator

 

There probably is. It's just a thermistor, so you'd have to figure out what its resistance is at low temperature and place a resistor of that value in its place. I'm not sure what the temp threshold is for charging system shutdown.

 

I can't see this cutting off the alternator, probably a short from within the alternator or a bad battery

 

The PCM reads the BTS. when it shows hot, it will shut down the alternator field wire to prevent overheating/gassing the battery