I use the copper method with MIG and have good results. The problem with filler disk or simply welding up is shrinkage. Heat does cause warpage, but the shrinking effect of welding is more of an issue in my experience. If you dont use the filler metal, just take your time and do the small spots untill the hole is full.
If you go with TIG or Oxy/Act welding you can reduce warping/shrinkage. With either of these methods, you can actually heat and hammer out the filler metal so that the shrikage is aliviated. With MIG, the wire is too hard for this. That said, I have never tryed these......would like to some day when I can afford a TIG machine.