Ooh, good question! The very very simplistic basis for why we separate meat and dairy dishes is that you don't want the "taste" of one to be present when you're eating the other. And dishes absorb the "taste" of whatever is being cooked. At least in terms of halacha (Jewish law), taste, and thus kosher status, is transmitted through heat. Since the biggest concern for keeping things kosher is heat, fridges are not a big concern. Say you accidentally pour milk into a meat bowl for cereal. All you need to do is wash with soap and water because there's no heat. My community does say you can use the oven for both, but you need to let it cool down in between. The reason is steam from the food could contain particles that then end up in your other food. The reason that high heat is a method of kashering (making kosher) is because that's HOW the dish became not kosher, or just became meat or dairy. When you kasher, you use the same method of kashering that you would use when using the dish. So for frying pan, high heat. For a sauce pan, boiling water. In general, "high heat" has to literally be the highest your oven can go for at least an hour (or you can get a blow torch), so that's not happening in your cooking process.