The only time I've ever had overheating issues on mine was during heavy track or autocross use in mid-summer, or when towing the 400-lb autocross trailer home with the a/c on in mid-summer. In addition, I haven't had a repeat of these problems since I recently flushed the radiator, replaced the cap, and replaced the t-stat.
However, the t-stat and the radiator cap on these cars do tend to go bad more often than with some other cars, so replacing them annually isn't a bad idea.
I personally wouldn't worry about overheating on a road trip, even at this time of year.