Ok, here is an initial effort to find the R4/R5 temperature set-point "offset" of an LTZ1000 (non-A).
There are two ways to find this offset: either use a fixed R4/R5 and place the circuit into an oven, slowly ramping the temperature until the voltage falls out of regulation, or use a fixed temperature (ambient) and adjust the R4/R5 ratio until fall into and/or out of regulation. Here, I'm using the latter technique.
The setup: R4 of a px-ref board has been broken out to a decade box, so that I can manipulate the temperature set-point. The meter is a Keithley 2015 at "medium" speed with a 10-reading moving average filter.
I've spliced the footage from the three cameras together, but I haven't edited the result into smaller chunks, so I'll just list a timeline of here:
0:00 Camera sync-up.
0:30 Approaching the ambient set-point from below (100-ohm resolution). 10.4k to 10.5k to 10.6k create steps of about 29uV. We are not yet in thermal regulation.
1:00 The 10.6k to 10.7k step diverges from the 29uV behavior.
1:30 10.8 to 10.9 to 11.0 create steps of about 77uV. We are now in thermal regulation.
1:45 Decreasing the set-point while so close to the regulation limit results in very slow response.
2:10 Switching to 10-ohm resolution. When just under regulation, adjusting the resistance has no effect (10.85 through 10.89).
2:30 10-ohm steps create steps of about 8uV when in regulation (probably, the steps are actually 7.7uV).
3:07 Using a fan to create forced cooling, to approach the ambient set-point from above.
4:00 10.86k is in regulation.
4:15 10.85k is in regulation.
4:24 10.84k is in regulation.
4:35 10.83k is in regulation (using the fan).
4:45 10.82k is in regulation (using the fan).
4:57 10.81k is in regulation (using the fan), but self-heating due to zener-current slowly pushes it out of regulation.
5:22 Self-heating drift of 8uV up from the 10.81k set-point, which also means the 10.82k set-point isn't with regulation at equilibrium.
5:39 Drift reaches 16uV, so ambient regulation must be above the 10.83k set-point.
5:55 24uV drift; 10.84k is not within regulation at equilibrium.
6:12 31uV, so 10.85k isn't regulated.
6:45 39uV, so 10.86k isn't regulated.
7:15 7.7uV times 6 steps would be 46uV. The drift is really slowing down as we cross over 47uV, so 10.87k isn't in regulation, but we are very close now (at ~23.5C).
7:25 At 48uV of drift, we verify that 10.87k isn't in regulation, and we verify that 10.88k is in regulation. We then decrease back to 10.87k, and the drift starts falling again, indicating the chip is cooling off, which verifies that 10.88k is in regulation at 23.46C.
So, at 23.46C, we drop out of regulation somewhere between an R4 value of 10.88k and 10.87k.
https://youtu.be/mbSmjaNA8xc