Using Celsius scale is just convinience in regular room-temperature metrology, so we don't have to say that temperature was changed from 292.15 K to 323.15 K, while room temperature kept at 296.15 K?
As for math, I used same approach to calculate alpha and beta coefficients just as it is common and well understood in resistance metrology.
This particular LTZ1000A reference does look fairly linear but it is not given and many other (LTZ-based) references are not as linear. Quadratic law fits bigger picture better. Sure, +237.6 C "zero" point does not have significant value here, more of an artifact number from my automated math script.
If you want to share RAW data, it is always good to include more details about actual experiment and methodology. I was interested in tempco of this 34470 clone and impact of different resistors on tempco results. Might try some other resistors in future as well, but for now I got my answers here. Full disclosure : don't have any 344* LCD-based instruments in my lab to contribute anything else or make tail or horns out of ACAL tests posted above and alike, sorry.
To me adding extra delays and pauses or running ACAL so often (which is not ACAL like on 3458A) sounds bit strange. Typical experiment run is using DMM for logging data for some time, and then if temperature or condition changes a lot, perform corrective ACAL. Usually always try to collect at least day or more of data when its about stability or noise parameters. But without more clear idea what you testing or expect to see in results it is hard to suggest anything specific.
One important thing forgot to mention - measurements of the 34470 module output were made with wires (both power and LTZ output) directly soldered to the module. Original connector with female sockets was desoldered. Voltage output wire was twisted pair PTFE-insulated copper with shielded connected to GUARD port of 3458A. Cable on the DVM end are terminated to bare copper spade lugs. LTZ1000A chip was covered with some packing foam on both sides with help of kapton tape
. Typical stuff when dealing with LTZ1000A-designs.