Dude, try running in Palm Springs. I ran 4.4 miles the other day in probably 105 degrees. It was pretty much the surface of the sun out there. I had a water bottle with me (and I never drink on runs) otherwise I would have died. I was crawling through the run. I wasn't even winded, it was just the heat. Do your best to PT before OCS without killing yourself in the home stretch, and when you get there, the fear of god instilled by the DIs will give you all the motivation to give it 110%.
As for treadmills, you lose the benefit of momentum when running on a treadmill, but you also gain the benefit of no wind resistance, so it is probably a bit easier to run on a treadmill. Also, people can usually push themselves a bit more on treadmills by dialing in a speed and working to run at that speed, whereas on the road, u slow when you tire. I use the treadmill to run at speeds I can't sustain for long runs to help increase speed, but nothing beats overall endurance like a nice long run on the road. If you can run 4-5 miles at like an 8-9 minute pace, then you should easily be able to push out a passing PRT run.