I thought the housing was cast, if that is the case, than you will need to heat the housing. Cast metals are hard to weld correctly. Sure, you can lay a weld down, but if you improperly weld cast metal, than it could cause damage. The idea is to evenly heat the cast metal before you weld.
If the housing is not cast than just disregard the statement above.
Now I have a question. If you weld your axle tubes to the housing, would the heat of the weld hurt anything inside the housing such as grease or bearings?