Uh-oh... First you mention white smoke and then overheating. Not good. Not good at all.
The 3.4 is notorious for blowing head gaskets (usually the upper side of cylinder #5); the 3800 less so. The 3800 problem is often bad lower intake manifold "spaghetti" seals. The intake manifold gasket is thick, hard plastic with grooves to accept soft, molded seals. Didn't work so well.
The 3.4 in my 94 made *lots* of stinky white smoke (see pic). The 3800 in my 97 Buick (since sold) didn't smoke but slowly lost coolant.