Here are some quick facts about tires:
1- Every tires operating (or I'd call it optimum performance) temperature is different. It is not brand specific, rather model specific (depending on the rubber compound, sidewall stiffness, thread pattern, etc.)
2- On a track you will be building heat into the tires, leading the pressure to rise. I would STRONGLY advise staying below 40 psi HOT! Meaning when you come off the track at the middle or towards the end of the session without the cool down laps.
Another fact to consider into heat building within the tire is the weight of the car. The less weight you have on the tire, the less strain the tire will have resulting in a less heat build. Considering I've seen an increase of 12 psi in a 3,250 lbs GT3 in summer heat, an M3 weighing over 3,600 lbs will build even more.
3- Over inflating the tire creates the risk of blowing it up. Even if you don't blow it up, the area of the tire where it makes contact with the road (also called: contact patch) is reduced. This will result in bad handling.
4- Under inflation of the tire will result in sloppiness caused by the tire not retaining enough pressure for the side walls to retain the rigidity. That is why when people let air out of their tires before a track session do not push their cars for the first few laps until their tires warm up and reach their optimum performing pressure.
5- Retaining the pressure of the tires below 40 psi HOT, experiment with the pressure. Like I said, every tires operating temperature is different so it will take some time for you to find the sweet spot.
What I would suggest is before going in the track for the first session, set your tires to about 35 psi cold. Go out for about 4-5 laps and come in hot into the hot pit and check your tire pressures. If above 40 let some pressure off. Towards the end of the first session before the cool down laps come in again and do the same.
Remember that as the day progresses the temperature of the track itself will increase with the air temperature and the cars that are on the track. So 40 psi HOT in the morning will not likely mean 40 psi HOT in the afternoon
Be safe and have fun.