Ideal rolling is rolling without slipping. Precisely, it is when the distance covered on the ground is equal to the arc length rotated through the circle during any time interval. Since rolling involves only static friction (as opposed to kinetic friction in rolling with slipping), the force between the tire and the road does no work. So we would expect that an ideal tire would not heat up. Real tires heat up a lot. It is easy to calculate the force of friction, and the work done (by measuring temperature of the rubber and pressure of the air before and after the test trip and acounting for the road heating the tire), and in this way calculate the total distance that your tire "slipped" during the trip. I am curious how close real tires are to the ideal of rolling without slipping.