I grew up with primarily wood heat and a budgie... He lived a good 12 years and alwas seemed healthy, despite living in the same room with the wood stove. I would think if you have a good clean flue, no major smoke events, aren't burning any chemically treated wood and and make sure the bird never gets the chance to get burned by flames or hot metal/bricks it should be OK... But that's from my experience not any other knowlwdge... Also, we had an air-tight vermont-castings stove, not a fireplace.