It's not good to be in such a condition for 1h, you'll be losing energy and you could get ill. 1h fighting to keep your body heat isn't going to be good for your health.
I'm sure it has to do with your schelude, as you said you go to the pool very early in the morning, and at least here, they plug off the heaters every day when closing, so the water will lose heat over the night. Consider changing your schedule, because you'll face this every day.
Personally, I'd be sure to stay near a warm water outlet.
