Arthur,
I concur with you that the user guide document doesn't mention Tdie/Tambient has to be kept at a constant temperature in order to get a correct S0 slope. For a given Tdie/Tambient temperature you will always obtain the same S0 slope values as opposed to obtaining an incorrect or negative slope when you fit the equation using readings at different ambient temperatures.
Another important thing to consider is how fast you decrease the temperatures to -40degC.
My email id is abhishekmuppiri@ti.com, do email me with your contact details so we can schedule a phone conversation to get this resolved ASAP.
Best Regards,
Abhi