I actually did do a test along the lines you suggest. About a year or so ago, I wondered how fast I could make a pizza and still have it edible. I concluded that I would have to use the highest possible temperatures for everything, and especially the dough temperature. I decided to use the imported "00" flour (Bel Aria brand), which I had been experimenting with for some time in an effort to replicate authentic Neapolitan style pizza dough. The 00 flour is low in protein (about 7.4% for the Bel Aria brand), and low in gluten, but, more importantly, a dough made with the 00 flour doesn't require retardation (refrigeration) and it is far less prone to springback problems characteristic of higher-protein, higher-gluten flours. For the yeast, I selected instant yeast since it has the highest rehydration temperature range of all yeasts (other than "rapid-rise" yeast, which I don't like and never use), and there is no need to hydrate it in water. I just mixed it in with the flour. The only other ingredients were water, some sea salt and a little bit of olive oil to oil a container in which the dough was to rise.
I put the flour and instant yeast into the bowl of a food processor and pulsed the processor to combine them. With the motor running, I added the water, which I had heated to 115-120 degrees F in a microwave oven for about 20--25 seconds (and measured with an instant-read thermometer), and processed the ingredients until a smooth dough ball was formed between the processor blade and bowl. As is my regular practice, I then added the sea salt and processed the dough until the salt was fully incorporated, and the dough was smooth and would pass the windowpane test. (In actuality, I could have added the salt to the flour and yeast to begin with, since instant yeast is more tolerant of salt and especially so if the yeast is first incorporated into the flour, but old habits die hard). I don't recall actually measuring the dough temperature (I wasn't as smart then as I am now), but I do recall that it was very warm to the touch, almost hot.
I put the dough ball into a lightly-oiled container, covered the container with plastic wrap, and put the container into a "proofing" box I had constructed from a Styrofoam cooler, a lamp, a standard dimmer switch, and some other simple electrical parts I had bought from Home Depot. The design allowed me to achieve a range of temperatures from room temperature to about 120 degrees F. At the beginning of the test, I had cranked the proofing box up to its highest possible temperature, about 120 degrees F, as measured by the instant-read thermometer. I had likewise set my oven temperature to its highest operating temperature at the outset of the test, to be ready for the pizza. I left the dough in the proofing box to rise for about 30-40 minutes, or until it about doubled in volume and my finger would leave an impression in the dough when I pressed it into the dough and removed it.
I then pressed and shaped the dough into a pizza round of about 9-10", dressed it in classical Neapolitan style, and baked it on a preheated pizza stone at the oven's highest temperature for about 6-7 minutes. (To save time, I had gotten the tomatoes, cheese and other toppings ready as the dough was rising in the proofing box.)
From the time I went into the kitchen and turned on the oven and cranked up the proofing box to the time I was seated at the kitchen table with a glass of wine, the total expired time was just under an hour. What surprised me most was that the pizza was quite good. Not as good as one made following the more conventional approach and more normal dough temperatures, but quite good nonetheless considering that the total elapsed time was less than 1 hour, most of which you just sit around waiting. Since my initial experiment, I have modified the recipe by increasing the protein content of the 00 flour somewhat, as by adding some vital wheat gluten or ordinary bread flour. I also tried using only high-protein, high-gluten flour, but the dough produced a crust that tasted like cardboard.
In anyone is interested in the specific recipe, I'd be happy to share it with you, so long as you promise not to laugh. I call my recipe a "last-minute" recipe, for those who can't or don't want to take the time to make a "real" pizza.