Your hand is conducting electricity and warming up the battery? 
No, neither really. Just to be sure I measured my fingers in the same positions I was holding the battery and with the same probes. With approximately the same pressure used to hold the battery, I'm 106M. With a lot more pressure, 26M. And the battery was cooling down, it had been in a warmer spot.
The whole theme of this thread (to me) is making assumptions without examining them and even resisting challenges to them. The original example was "I want a more accurate (cheap) multimeter and I'm going to judge that solely by the advertised basic DC accuracy headline spec". Now we have drifting battery voltages and assumptions about why that happens.
You see a battery connected to a many-digit multimeter with the LSD slowly counting down. You assume that the reason for that is that the ~150nA is flowing in a 1.5V/10M circuit is drawing down the battery. You see someone doing the same thing but holding the battery in their hand and the voltage is going up, you assume the reason is that the battery temperature is increasing. It turns out that there might be other reasons for these behaviors and unless you somehow quantify the effects that you attribute the changes to, you can't reliably assign causes to your observations.
With an AA battery, unless you can accurately (very accurately) measure temperature and also know how the battery behaves, thermal effects will probably outweigh all those other things by quite a bit. In this case, at near room temperatures, the battery voltage goes
down as the battery warms up and there is no discernable difference between the 10M and Hi-Z modes on the meter. If I hold the battery differently so as not to 'short' it with my 100M fingers the voltage changes (drops)
more quickly, presumably because more of my hand is in contact with it and thus it warms faster. This is not what I expected when I tried this out just a bit ago.
Things are never as simple as we want them to be.