Something important to keep in mind is how much land it takes to sustainably feed someone. If you Google "how much land does it take to feed someone", the results say that it takes about 1 acre to feed one person. 2 square miles is 1280 acres. This means that if the land is arable (farmable), then you could potentially feed 1280.
Because "the ground is mostly made of stone", this isn't arable land. That means plants won't grow without a lot of work. Also, it will be very dry—tundra is naturally quite dry (cold air doesn't hold water very well), and when that cold dry air comes in and becomes warm dry air it will be able to absorb more water, leaving the warm area drier than it was before. When that air leaves the warm area it will want to release its water, so the surrounding tundra might get a little bit more rain/snow than normal.
So to get anything to grow, people would have to do a lot of work to prepare the ground to allow plants to grow. Then, they would have to continually bring in all the water that the plants need in order to grow.
Even if you could prepare the ground and bring in enough water, I have no clue what these conditions would do to plants. I wouldn't be surprised if having the temperature stay about the same even at night would seriously mess up their growth cycles. Also, don't expect plants to be able to grow at full speed year-round—even though it will be warm in the winter, the amount of sunlight they get will be minimal. This might actually cause them to be unable to survive the winter, as the temperature will not let them go into hibernation but they will not get enough light to live.
However, since we're already dealing with a magic stone, you can handwave as many of these problems away as you wish.
In summary, there is enough land to be able to support over a thousand people. If the stone does nothing but make it warm, it would still be a massive undertaking to be able to live there. You can make a decision about how livable you want the area to be, and then allow the magic stone to help plants grow enough to make up the difference.