I use the word "Appliance" because there are many different types of wood burning heating sources for a home. It could be a fireplace insert, freestanding stove, wood pellet heater, or even a wood burning furnace.
When buying a home with any of these appliances your insurance company will surely have a few extra questions. To help avoid headaches after you have a firm offer, have your agent ask the seller for a WETT certificate. Most licensed installers are WETT certified, so if the appliance is newly installed, the invoice will normally do. You may be surprised how many homeowners actually have this information with their home file.
If they don't have an invoice or WETT certification, and the appliance looks a little suspect, make a conditional offer pending the seller produce one. If this isn't feasible, ask your insurance agent to come inspect. A good agent will know if there is any concerns or if the unit will need a professional inspection to qualify for insurance.
The worst case scenario is that it doesn't pass... not the end of the world. Unless the wood burning appliance was the main reason you wanted the home, you can easily remove and/or cap the fireplace and enjoy your new home just the same!