I haven't had much luck heating them and cooking on them. I find them more useful cold. We keep a couple in the freezer. I love putting sliced radishes or cukes on the cold stone and snacking on them with a beer on a hot day. You can also use them cold to "cook" seviche. My girlfriend uses two to sandwich slices of watermelon which end up with a similar texture and flavor to prociutto, believe it or not.
I heated mine up on my gas stove top without any problems yesterday. I didn't cook on it though. I'm really liking the "using it cold" idea though especially for the seviche. My wife travels to southwest on business several times a year and she loves seviche. You have a recipe you'd like to share using the stone? I've never made it but have wanted too.
I don't write recipes down much but I remember my process. I take nice fresh fish, usually scallops or wild salmon but whatever you can get fresh is best, and slice about 1/4 inch thick, toss in a bowl with your acid and possibly other seasonings then arrange on the block. Its OK to touch or even slightly overlap. Put the block on a plate to catch liquid. At this point since we have two we put another block on top and put in fridge. If I had one I would put a piece of plastic or foil on top and place a brick on top to speed things up. With one block that is more or less full I would turn the fish over in 30 minutes, and see how much it "cooked" so you know when to check again.
You can use whatever acid you want based on the flavor profile you want: lemon juice, lime juice, your favorite vinegar. I have even used Kim chi juice. You just need enough to coat.
I tend to add any other ingredients, especially raw veggie like diced onion or chili peppers after to save room on the block and prevent extra water from being drawn out of the veggies.
One thing I did was a fish taco inspired appetizer. I think I used halibut. I used lime and lime zest on the block and then when done tossed with diced jalapenos, red onions and other seasonings. I served it on fried polenta chips but freshly fried cut up tortillas would be great too.
I have also made a quick gravlax with salmon and dill.