my guess is 30 mins or so. similar things happened to me at daytona (computer issue) and the fix was to roll up the windows, lock the door and wait 30 mins. the computer reset itself.
i can confirm some of this, i think. my last track weekend my tires were on their way out and in sport+, the only way i drive on the track, i was drifting all over the place towards the end. not sure if my reflexes were that amazing or the computer was that slow (or allowing it though it never had before on any track so i honestly beleive it was the tires), but i caught it before the computer (nanny systems) every kicked on.