to weld aluminum that thin you would need a TIG machine. And a whole lot of know how.
Aluminium conducts heat very well, so the heat generated ahead of the weld means you constantly have to adjust current. Also, most "aluminium" that you can buy is actually an alloy of some sort. Depending on the metal, it may want to resist shrinkage after welding, making it crack. Sooooo. If you know what you are doing, go ahead and weld it, but if you knew what you were doing, you wouldn't have asked.
I would suggest you try brazing, with an aluminium filler.
Here's the catch:
The filler's melting temp is rediculously close to aluminium's melting temp, so go slowly and make sure you have some pieces to practice on first.
IMPORTANT: Clean the surfaces you want to braze really well, aluminium oxidizes really fast and you can't really tell just by looking at it (and it's really annoying because aluminium oxide melts about three times the temp that aluminium melts at. Not good!). Use a wire brush, then a little bit if distilled water on the surfaces, and dry it and immediately start the brazing process.
Oh, and you will still have to worry about stress cracks during cool down, so try to bring the temp down slowly.
Good luck! dont be discouraged if the filler wont adhere at first, or you melt your piece. Just keep practicing, and you should be able to get the hang of it.