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.
 
