Sorry James N.....do not agree on your thin insert idea. YES, they do warm up faster, but if you are running in the heat and/or high traction, you will overheat the tires....especially in mod.
90% of the time, when running stock, you can use the thin inserts and be ok. With mod, too much heat builds up in the tires, as they tend to squirm with out the sidewall support of a thicker insert.
In high heat, high traction - HPI Blue insert (yes, these are on the thinner side0.......or...my favorites.....Sorex Firm Type A or B thick inserts. Still an airgap between the tire and the insert, but not as much.
To answer your tire question J. Werner....Try Sorex 32 or 36 with Yok Firm inserts. What is the track temperature? Are they using any traction enhancer?? Mod or stock?