what year is it? have you changed your LIM gaskets yet? may save yourself some time and money down the road to do it all together. its an all day job, but most mechanics are going to charge you anywhere from $700-1200 for the labor. i would do it all at once, since the t-stat is such a pain to do anyways on the 3400. might as well get the new redesigned LIM gaskets in there while you have it apart. if they arent leaking yet, its just a matter of time until they do.
EDIT: i see you have a 2000. check out your LIM gaskets and see if they are leaking. if they are not leaking externally, there is a chance that they are leaking internally as well. look at the underside of your oil filler cap. if theres a milky substance there, you have faulty LIM gaskets. also, look for the notorious dexcool sludge in your cooling system (rad cap, overflow bottle, hoses, etc.)