StarSpecs get greasy after 10-15mins regardless of temp, no way around it. The StarSpec sweet spot for my car and driving style was 37psi hot.
NT01s need to be driven at a higher slip angle and ideally -2.x camber or more. 38psi hot. If you try to drive them like the StarSpecs they'll be gone in 2-4 days. The first time you run them they'll be slippery for a couple of laps (just once) and then they'll remain at a set grip level till you cord them.