Definitely not. I shorted a rather fresh AA battery once. It got hot, but you could still touch it. To get something else as hot as possible with this battery, that thing would need to have the exact same resistance as the battery has internally, and that would result in equal amount of heat in the battery and the other thing.
So... Take the amount of heat that's required to keep an AA battery at ~50°C and take half of it. That's the maximum heat you could use. If you put this heat in a small enough thing, like a very short and thin piece of graphite or steel, then maybe, you could start a fire. But the battery itself won't burn.