I can go up 2 degrees an hour in full sun, usually about 1 degree an hour overnight.
The natural gas costs me about $100 for a whole summer of usage. I probably run the heater for 100 hours a season, and a 240K BTU pool heater uses about 2.5 therms of NG per hour. At $0.45-ish per therm, that equates to just over a dollar an hour.