I've never herd of the sun trick, I have heard of VERY skilled welders being able to manipulate the metal by heating with a welding torch and then putting water on it. I thought the trick was how and where the metal was heated. I'm not sure heating the entire area and cooling the entire area will do much good. Since you have gas fumes in the tank, forget the welder. I don't think the sun is hot enough to do much good, but I could be wrong.
Most metal, if it is not creased, retains a memory of its initial form. I would think a suction cup / dent puller (the stuff advertised on TV) would work as well as, if not better than, the sun and ice trick. Nothing is going to work though if the metal is creased.