Even with careful TC compensation it might take some time to stabilize, as it takes time to get the final temperature differences.
I very much doubt it matters in 5.5 digits meter, those effects completely dwarfed by 10ppm resolution of the A/D in here.
Having so much trouble with the ADC / amplifier, it might have been easier to swap the display to the parts donor unit.
But then we will not have this article and thread, eh? Also my meter have shattered high-voltage divider network, and who knows what other problems.
The heated references LM399 / LTZ1000 usually are rather fast in getting there temperature.
Yep, getting heat to reach equilibrium with everything around them is still hours. Hence I never turn off my 8.5d meters, except for service/relocation. And LTZ can take days to reach <0.5ppm from previous value, if stayed cold for long.