Looking at the 121's measured voltage during the transitions between the two extremes, we can see the most error. I wouldn't be too surprised if I actually thermally shocked it, say for example, leave the meter in the car during winter and bring it into the warm house and try to use it, we would see something worse. The change would be less but the ramp would basically be the thermal mass of the meter.
When I was trying to shock(ish) some of the other meters, that UT181A has proven to be one of the more stable meters. I doubt it has anything to do with the changes I made to improve it's front end. It could just be an odd ball meter.