Correct welding procedure is to slowly preheat the components before welding then slowly cool them after welding. For most items welded on a ship, covering the component with a fiberglass fire blanket just after welding and leaving it to cool slowly is good enough. If the component is particularly large or has a complex shape, it is better to preheat it, if possible.
Welds almost never fail at the place where the material has been melted. Most of welds fail in the "Heat Affected Zone" (HAZ) which is the metal next to the metal that melted due to been heating to high temperatures and rapid cooling.