I wouldn't recommed lowering the top if the weather is below 60. If you must warm up the cockpit full blast until the plastic doesn't feel so cold from the outside. You will get a wrinkle in the plastic that could take weeks to stretch out again with these temps.
By the way, congratulations! man that reminds me of my first sports car purchase. I'd never applied for a loan before. Wasn't sure if I would be approved. I don't think I slept a wink the night before. I was about to cash out some stock (a bad idea) if they didn't give me the moolah because my buddy was selling me the car at half of bluebook. Then the next day the Bank offered me like four times of what I was asking for. Then came the mods...