I did try to do some testing on heat loss and recovery time, but decided I would not be able to do anything that would really answer the question, the only answer I got was to a question I never asked. I have an older version of a Bakers Pride P18 2 decks, 110 volt, 3 elements, but only one thermostat and no way to turn off individual elements. Original equipment is 1/2 " stones, and I bought 1 inch corderite kiln shelves that I cut to fit. On the top deck I put a temp sensor, then the 1/2 " stone, then the 1 inch stone, on the bottom deck I put just a 1 inch stone - so the upper deck has 50% more stone. I heated it up till the lower sensor and the ir temp on the top of the top stone were as close as they could get ( 680 below the 1/2 stone and 690 on the top of the 1 inch stone.) then I loaded an aluminum pie pan with 1 or 2 ice cubes on it, and closed the door and let it stay for 3 minutes, then took out the pan, then checked the ir on the top of the stone every 3 minutes until it recovered, and monitored the temp at the bottom of the stone which never moved. The first time it dropped about 50 degrees on top of the stone, and recovered 45 degrees in 6 minutes. The second time, ( 2 ice cubes ) it dropped 110 degrees and took 9 minutes to climb back to within 5 degrees of starting temp. When I did the test on the lower deck, it dropped 110 degrees and took 9 minutes to recover. I was going to repeat it a few more times, but realized there were too many differences. First, the lower stone never gets as hot as the upper deck, second, the lower stone was 1/2" further from the upper element than the upper stone so wouldn't get the some heat from above as the upper stone. The best way to deal with both would be to use pieces of kiln shelf to elevate both the top and bottom stones of the racks so they were the same distance from the upper elements, but then they would be different distances from the bottom elements. I also realized that the temp drop would depend, in part on exactly how dry I got the pan between tests, the size of the ice cubes, and whether they stayed close together, or drifted once the pan was in the oven. The one positive conclusion was that when you use a wooden peel to take the aluminum pan out of the oven it will be about 500 degrees, and if you leave it on the peel for a few minutes while you check the temps in the oven, and use the ir on the stones, then write all that down and a few minutes later go back to the peel you will find one or more of the following : burn mark from the pan, glue failure because it got so hot, and shrinkage from drying out the wood - if you are lucky and get all three, you will have more of a comb of separate pieces at the front, and one solid glued shape at the rear - though I have several extra peels so no real loss.
I was going to measure the drop in temp when making pies on Sunday, but I had a colossal failure - it turns out a stromboli works because there is dough on the top and bottom. If instead, you cook a pizza 1 1/2 minutes with a stone around 700 and you try to take it out to turn it around, and instead it develops a hole, and the cheese gets stuck on the peel and causes the pie to fold over on itself - it generally ( well I only tried it once, but I still feel comfortable in this prediction ) won't fold over exactly in half like a stromboli, and instead a part of the cheese topping and sauce from the pie will fall upside down directly on the stone, which I did mention was about 700 degrees, and at that point, you can try to get as much of it on the peel as you want, but the only real things to do is turn on the kitchen exhaust fan, and start taking batteries out of smoke alarms - since it takes a long time for 1 1/2 inches of cordierite to cool down.
Finally, to the question of the stone getting hotter than the oven, I assume the broil element is hotter than the oven and am no expert, but would guess radiant heat would get it closer to the temp of the element than the surrounding air.
