Is the pan steel or aluminum?
If it's aluminum then the whole thing might need to be heated and then cooled slowly. Just about anything cast gets cranky when brazed/welded.
If it's steel, I'm not sure what's going on, other than that there are a TON of residual stresses from stamping that are pulling it apart after what is basically localized heat treating. Also yes, you may be getting it too hot, and going past the upper critical temperature, where the carbon dissolves into martensite., and when it cools too rapidly in that state, it will definitely crack and be extremely brittle. Cooling slowly is the key. Though, similar things can (well, do) happen with welding too. This depends on a lot of what alloy of steel it is.
Given your pan is cracking and not the plug, the plugs weld-ability is fine.
Without being a super expert on welding/brazing, nor knowing exactly what the base materials are, I can only suggest slowly heating the whole piece, and slowly cooling it back down, I also think you may be getting it on the too-hot side of things.
Brazing is plenty relevant today, and a lot of materials are more easily brazed than welded as it doesn't melt the base material. The only difference between Brazing and welding is temperature.
Welding temperature is classified as any temperature high enough to melt the base metals together.
Brazing is done generally in the 1200°F-1600°F, so if you're getting the base metal hotter than a dull red, you're getting it too hot.
Soldering is a filler metal that is liquid below 850°F, basically low temp brazing.
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