Like the other poster said. If it's installed correctly and used correctly it's just as safe going to bed with the wood burning stove going as it is with a natural gas or propane furnace going at night.
They both have fires inside the box.
What causes house fires from wood stoves is usually the misuse of the wood stove, getting it too hot, not cleaning the creosote from the chimney and pipes, and not having the stove installed correctly.
I've slept with my wood stove going last night and I've done so in the past before without thinking twice about it.
I installed it myself and I installed it correctly. Make sure you keep the wood stove at the minimum clearances to prevent walls and other combustibles from catching on fire.
It's okay for the wall behind the stove to get a little hot but not really hot.