Hi Stijn,
I have removed quite a few stones from their housings...
The oven trick will work. At 60 degrees, maybe 75. But I have had very good luck with very hot water, maybe about 60 degrees (!). Don't start prying at it with anything, you'll just chip things up.
Run it under the hot water, try to get it in between the stone and the wood. Start wiggling it, if possible. Then put a kitchen towel on the edge of your counter (you may want to unscrew the lid for this), turn it upside down, make sure your hand is under the stone, and tap the edge of the box (the top edge...) flat against the edge of the counter. The weight of the stone combined with the force of the strike always gets the damn things out. (Just as easy to do this after being in the oven but with water everything is not so hot to hold)
Good luck!
regards,
Torolf