durodi, Interesting hypothesis, but I don’t think it works the way you propose. Did you visit the two sites I recommended? There the physical deformation of a crystal and the resultant charge generation is clearly described.
A quartz (piezoelectric) crystal must be deformed along a particular axis in a well-defined direction in order to produce a voltage.
A quartz crystal immersed in a hot gas will be bombarded by rapidly moving molecules. But they will impact on the crystal from all directions, and therefore exerting a force on the crystal in all directions. The result will not be any vibration, deformation, or voltage generated. So there would be no conversion of heat energy to electrical energy.
Nice try, durodi. I encourage you to continue your searching. This is how new discoveries are made.
Cheers,
Bobbywhy