Wow, yeah, a pictures worth a thousand words. That is definitely different than the one my sister just bought.
You very well may have put your finger on the problem here
(pun intended)
If you could put your finger in there for more than a split second without pain then it is gonna take a lot lower temp switch than 140* to make the switch close! I bet the new switch SBI is sending is a lower temp than the one you have now. If the new switch is the same temp range and you have the same results, I'd be on the phone with SBI about it again post haste. From what I hear SBI (drolet) has been pretty good to work with when people have had problems.
If it were mine, I'd wanna to fix it today, I would jumper the thermoswitch and make it run as long as there seems to be warn air coming from the vents, that would be a quick/easy test to confirm your theory. Just clip on a jumper wire (something heavy enough to take 5 amps or so, (14-16 gauge wire would be fine) or you could even wire in a light switch so you can easily flip on/off as needed until you get this sorted out.
The switch you had out yesterday had white wires on it, yes?
If it had red wires then that is the high limit switch, (according to the current manual)(there should be an electrical drawing in the back of your manual) it cuts power to the damper control motor if things get too hot until the blower can cool things off. The high limit switch would be NC (normally closed) until it gets to 160*, then it opens up.
The fan control switch is NO (normally open) until it gets to 140* (or whatever temp switch you have) then it closes until the blower cools it back to 120*. Do you have a multimeter that could be used to test the switches? I would think you could use a hair dryer to heat the switch for testing