Mujitsu and Tairaku's Shakuhachi BBQ

Hello,

Not sure if this question fits in this forum so my apologies if it's misplaced.  My question is in regard to Shakuhachi storage.  I live in a house that is drafty, cold at night, and frequently gets heated by a wall heater.  When I finish playing I wrap the flute in a two plastic bags and a fleece sac.  Im a bit concerned that the fluctuation in temperature will crack the flute.  Any help and guidance is much appreciated.  Thanks.