I have yet to bring the GT out to the track. I have a date in May. If you can find someone with a pyrometer at the track they would likely be more than happy to do tire temps on a GT.
I would normally start with +4 lbs front on a front engine car. For this car I too have no clue. I will start with 32. Note all of the following is my experience with the Goodyear SC tires....Hoosiers are a different story.
If you can get the tire temps, it goes like this. Start at 32psi run a warm up session 20 mins or so. You shouldn't hurt anything as you are just getting warmed up say 70-80% of your limit.
Here is the routine:
Starting at the outside edge 150 mid 130 inside 150 = Add air 1-2 psi
145 mid 165 insde 150 = reduce air 1-2
Most anyone with a pyrometer will be able to help you make the adjustment.
Now if you get something like this, it's an alignment issue you will need to science for the track:
Outside 210 mid 180 inside 160 = I would add air to compensate for the day, but the real problem is not enough negative camber. You won't be solving this real easy at the track without some special gear. Record this data for a discussion with your pro alignment specialist later.
If you have no way to check temps try this:
Look at the outside edge of the tire. You will see little triangle shaped arrows above the Goodyear logo and the two lines above that.
If you start to rub the arrow off while cornering...ADD air...try 2psi. Find some way to re-mark the arrows,( pen, marker, chalk. )
If it still rubs off , add another 1 psi until the wear does not go past the tip of the arrow. Ideally you want to wear right up to that tip of the arrow.
This is what the Goodyear guys showed me one time at a track day. Made sense and works well enough unless you are Michael Schumacher.
Each track will likely require a different psi. On the filp side, you may be able to let out a pound or two if you are getting no where close to the arrow.
You will notice a 2 psi difference in the way the steering feels and how it pushes or not. Nothing scarey, just a bit lighter or heavier feel.
I think the car is farily forgiving, so unless you really plan to push it through the corners or breech 150 for EXTENDED periods of time, you should have an enjoyable ride with no worries. I don't do back to back sessions, so I take the time to check the tires when I get out of the car. The car is fast but extened 150 is almost never seen at most tracks in the drviers school configs. Sebring, TMS, certain PIR configs would be exceptions.
Ps: 32 is the stock cold setting, you will be much higher after your first session. The +1-2 or (1-2) applies to current psi at the time you check it. Overnight it will be cold again in the morning, and a +2 will read maybe 33.5 - 34 when cold.
There was a post awhile back with some alignment specs for track days. You may want to search for "Track Alignment" I don't recall if it had listed the tire pressures as well.