Clamp the heat-absorbing sink, or backing bar, to your thinner metal. The backing bar will absorb excessive heat that the metal is exposed to during welding and will reduce the likelihood of warping.
Set your welding tool to the voltage and amperage settings required to weld the thicker metal. While these settings are more likely to warp your thin metal, without them, you simply will not be able to weld the two metals together with any integrity.
Fire your welding torch. Allow a pool of molten metal to form on the surface of the metal.
Experiment, while welding, to find the welding technique that gives you the degree of penetration that you need. Determine whether you should whip your welding tool in a zig-zag form, which will give you a wider weld and relatively little penetration into the metal or whether you should hold your welding tool in a straight line, which will give you deep penetration and a narrow weld.