If you short the sensor wire to ground the fan should come on, or if you turn on the A/C.
If the fan does not turn on you have the same problem that we all have.
When the bottle overflows is because the coolent is too hot, it is boiling and then turns to steam and the presssure builds and wants to leave the system.
By cooling the coolent it does not boil over.
I do not at this time remeber what relay turns on the fan for the low speed but it has a green wire and a gray wire on it.
Just like the high speed it has a green and gray.
I do not remember if it is light green or dark.
Your problem most likley is not a bad thermastat.
The fan would still come on, bad thermastat and all.
Update on my end, I added another relay to turn the fan on when the a/c is on. I did not have to, I just wanted it to turn on whenever the a/c is on. Just like it use to.
If you need anymore help let me know.
John