I sew in a cabin which is fitted with a wood burner, a few years ago it caught fire. Didn't entirely destroy everything but stuff was very badly smoke damaged. I'm now paranoid about the risks and double check everything is turned off. I also have a webcam and baby monitor (because it's separate from the house).
there are fire extinguishers in the house and cabin, just in case. Make sure you get the right one, I'm not sure about elsewhere, but in the UK they suggest powder because it covers class A, B and C fires. I also have a blanket in the kitchen.
you can't be too careful and it's best to be prepared.