Preheat/postheat the mass has other benefits as well as heat is pulled away from the weld by the surrounding steel *much* faster than by the surrounding air.
To be really sure you should cut the weld area out from the surround steel and let it cool slowly---then you can weld it back in, grin...
This is an issue in blacksmithing/bladesmithing as well when people find to their dismay that a nice cold vise or anvil can "quench" a hot high carbon piece with nary a visit to the oil or water bucket!
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Thomas
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