Let me preface this by stating that I don't actually have any special knowledge of the art or criminal world beyond what I've seen in the movies, so the following is pure speculation.

I could imagine that if a thief's motive were purely financial, he/she could ransom the painting. "This is a priceless piece of world heritage that is heavily insured. Send XXX BTC to this wallet or I'll burn up the painting and send you its ashes."