Tested LM399 out of Keithley 2001 for operation at sub-zero temperatures. Perhaps this is interesting for someone other than me.

Device is SL40057 IC-257 (custom Keithley P/N for selected LM399) date code 30 week 1991. Heater part of LM399 was not connected to anything, and "zener" part biased with +24V from Keysight E36312A and 11.1kOhm BMF resistor (static at ambient temperature). Output (kelvin-connected) from zener circuit was monitored by trusty Keithley 2002 DMM.
Run took about 1 hour, and temperature of GM cooler cold-tip with attached LM399 (without plastic casing) was reduced from ambient +27°C to -262°C.

Reference stopped working at around -185°C or so, with current drawn from PSU reduced down to 770uA (vs 1.45mA nominal) and output voltage going over 8V, all the way until 15.4V.

Crude logging equipment setup:

I guess there is too much going on inside LM399 to operate this much far out of specified 0°C

Next specimen is obvious LTZ1000...