I don’t know. You’re connecting the two batteries. The one that has more voltage will charge the battery with less voltage. And because it’s just a strip of copper between the two, without significant resistance, it’ll happen fast. The thing limiting current flow is probably the internal resistance of the battery itself. And for example alkaline batteries, you’re not supposed to charge them.
I haven’t tried what exactly happens. AA batteries aren’t as powerful as for example Li-Ion batteries. So you’ll probably be alright. Maybe in the worst case one battery gets hot and smells funny. But I don’t think this will cause a proper fire. If it’s only a bit, it’ll get a bit warm and you waste some energy, that’s probably it.
If you connect one in reverse I’m not so sure anymore. I once had a rechargeable battery that was connected in reverse get really really hot and bulge. Once you do things like this with Li-Ion rechargeable batteries, I think you’re in the realm of starting a fire.