That depends, obviously it's the tyre surface that's in contact with the road. If you follow F1 or V8SC fore example, you'll find that pressures are very critical for tyre life and even single-lap performance. Internal temperature determines how much pressure is gained from cold temps, and under/overpressure can cause very significant wear and handling issues. Not to mention there should be some effect as to how much and how quickly surface temperatures drop between corners (with slicks anyways).
Alonso let Vettel pass at the hairpin, in order to DRS him back on the straight. His rears were so badly worn that even though he planned and executed it properly, he couldn't keep up in the corner exit.