As JFP said, flat-spotting tires is a holdover wives tale from bygone days.
When tires were exclusively steel belted, flat-spotting was an issue. But, tires today use synthetic cords such as nylon, polyesther and kevlar. These materials (in this application) do not have a permanent memory and the tires will come around (no pun intended) as soon as they are up to temp.
I wish I was the guy who came up with tire pads. If I was, I'd be driving a Lambo instead of a Porsche.
