18 inch tyre pressures

[RosscoMK3]

So you get them to run a higher cold pressure to achieve a lower running pressure while subject to extreme friction on the track? Am I on the right track here?
It sounds like you have plenty of experience and I'm always keen to learn something new. My only track experience is with the two wheeled variety.
I tend to drive my car on the road for the most part and usually for no more than 30 minutes at a time. How would this affect the running pressure and grip?
Would it be fair to say that the cold pressure of a tire is less important than the running pressure during the intended use?
I was under the impression that maximum contact, while maintaining the shape of the tyre, was best for handling and feel.