My sidewall says 40 PSI max (measured with a cold tire), so as an experiment, I rode aggressively on a hot day (about 90F) until the tires were hot, then put exactly 37 PSI in them.
My thinking is that even on a hot day, with the tires hot from riding hard, they won't go over 37 PSI. Since it's usually cool here (60 to 65F), and I don't usually ride aggressively, it'll usually be a bit below that, so I shouldn't have a problem with too much pressure in the tires.
I'm hoping to increase my fuel mileage a bit in doing this.