The issue with welding stainless is that you aren't going to be able to do it with a stick welder. My experience is that they use a TIG (tungsten inert gas) welder. When welding stainless and all sorts of other metals, you cannot let oxygen come in contact with the surfaces to be joined. In regards to the heat, charcoal isn't going to get hot enough to cause problems with a stainless drum. Welding temps are in the 10k* to 20k* range, which is considerably hotter than your grill wil get.
There are others here that are much more versued in the details of welding than I, but this is the general issue.