When installing a wood stove you should put a heat shield on the wall behind the wood stove.
With the heat shield it's recommended to keep the stove at least 36" away from the wall or any combustible objects.
It's okay if the wall gets a little hot but not enough to where it will burn you hand when touching it.
If the wall is getting too hot to keep your hand on the wall then you have the stove too close to the wall and should move it away from it.
The further away you can get the stove from the wall the better.