Hi Max,
The baths we use are a type of oil, but I know there are other chemicals that can be used as well. It depends on the range of temperatures and how fast you want the bath to transition and stabilize.
If the voltage for the reference goes above the requirement you mentioned, you will see linearity issues. So yes, that can be a problem.
Another potential problem that is sort of related is voltage compliance of the IDAC. If the voltage developed becomes too high you will begin to see issues. The voltage compliance is typically AVDD-0.7V (shown in the Electrical Specifications table.) The effects are illustrated in the graphs shown on page 16 and Figures 15 and 16.
Best regards,
Bob B