Some answers, you may get conflicting ones.
Selfbows do have a limited life, how long is dependent on many things, how it's made, how it's handled and shot and how you store it. Osage can be too dry, but it's not as critical as with some others. Usually, bow either break or chysal, then break or go out of tiller in another way and break, eventually. I wouldn't keep it in the area of the wood stove, but that's just me. Mine are stored in an unheated garage, not ideal maybe, but so far, so good.