As I'm sure you know, tires designed for cornering are often not great under hard acceleration. The stiff sidewalls limit traction under heavy power. Those same stiff sidewalls keep the tire contact patch accurate during hard cornering.
Also, quite often, high performance tires achieve more grip once warmed up. The degree to which "warm up" is required depends on the tire. Many street tires need just a little heat for good traction, and will get really "greasy" on actual track days.
Contrast that with DOT street legal race tires. They often need somewhat more heating to work well, and can be very slippery when cold.
Of course, all of this depends on the design.
As I mentioned, I prefer the more sticky tires, (and performance brakes too) both require warm-up, but are an absolute joy once there.