Retired schoolteacher, sculptor, and carpenter
That just looks to be great fun. . If you want to use temperature, an old boy showed me how to do that by heating it up pretty toasty (not so hot you lose temper), then immediately quenching with ice water. That should shake loose any adhesions. If you want to go the chemical route, the BEST I've ever found is called Sili-Kroil, made by the Kano Corporation. Definitely clean all that off before expecting it to hold another bit in there. Once out, I'd be checking for any minute little burrs on either the bit or collet. 1000+ grit wet or dry sandpaper can help with that. And finally, as others have surely pointed out, never put the bit shaft all the way to the bottom of the collet assembly, always leave about 1/8"to prevent this foolishness from recurring. Good success to you!