After turning on the pilot, turning the gas control knob from pilot to on setting, then when adjusting the temperature dail, this is when then water heater turns off.

Check/clean pilot orifice.

By turns off I assume you mean the pilot goes out, right?

By turns off I assume you mean the pilot goes out, right?

Correct, the pilot turns off.

Many times the pilot lite is to weak/small to sustain itself during ignition of the main burner. Check/clean pilot orifice.

Trying some detective work here. Turn the temperature dial up to HOT before you light the pilot. Now light the pilot and turn the knob to ON from PILOT. Tell us exactly what you observe in the pilot flame, keep your eye on it but not near it. I'd also follow hvac's advice.