As one who has been a welder (a very long time ago) and who still has a good friend in the business, I'll caution you that as others have said, welding aluminum takes special skills and a tank adds extra requirements. If you can find someone to do the work it will probably be very expensive and have no guarantee.
I absolutely agree with Gary. It is very unlikely that a tank that was broken by freezing would only leak when hot but fittings are a very different matter. I locate a suspected leak by fastening a small piece of paper towel or tissue around or to the possible areas that could be the source, then pressurize the tank for a short time and check each one for signs of dampness.