Mine seems to be around 0.030-0.034 inch. The key thing is to check the temper. You want to make sure it is "O" rather than something like T4 or T6. O means is it annealed and will be easy to work. A common alloy will be something like 2024-O with the first four digits designating the specific aluminum alloy. FYI, check scrap metal vendors. They often have steel, aluminum, and stainless steel sheet metal remnants at a fraction of the Home Depot price.
If you are concerned about burning holes in it try putting a hot coal on a couple layers of aluminum foil and see what it does. It will be a very conservative indicator because thickness goes a long way to burn-though resistance. Al melts about 1215 deg F (some alloys are different) but you will lose most strength well below that temperature. If you opt for the very thin aluminum you could always line it with heavy duty Al foil to improve burnthrough resistance and keep it looking nice.
Also keep in mind that if you plan to hammer it into the dish-shape it will get a little thinner during forming. Also, very thin aluminum will distort more easily during later handling.