The problem with one or both AA cells getting shorted out and overheating seems to be a design flaw in the battery spring clips. On my meter the clips have sharp inside edges that can cut through the plastic wrapper of the AA cells as they are inserted, or perhaps as the enclosure halves are screwed together or if the meter is dropped/knocked.
This causes a short circuit at the negative spring clip because the metal cylinder of the cell (under the usually thin plastic wrapper) is connected to the positive terminal.
This has just happened to me after the first battery change today. Fortunately I smelled something hot within a few minutes and realised it was coming from the meter, which I hurriedly unscrewed and took apart. One battery was so hot that the plastic wrapper had blistered and I had to yank it out with pliers. The affected battery has obvious nicks in each end of the plastic wrapper. There doesn’t seem to be any damage to the meter, fortunately.
I’ll be putting a wrap of tape around the negative end of the replacement batteries to prevent this, and trying to grind off the sharp edges. It might also work to clip off the spring arms at the negative end of each holder and rely of the plastic enclosure to hold the cells in position.