You'll definately know when you have a blown HG. You'll have a white smoke comin out of the exhaust, a sweet smell, and your car will run like crap, because you will have a mis-fire. IF you take care of your car you should be fine. Yes, the 3.8s are notorious for the HG's, I even blew mine on my 96' but honestly, it was the best thing to ever happen to my car PERIOD.
I say that because I learned so much about my vehicle, and did about 99.8% of all the work by myself, with barely any mechanicing experience at all. Don't be scared about blowing your HG's, it's an experience that most of us go through with these engines. If you were to do any changing at all, I'd look for a set of 96+ heads for the 3.8, because they (supposedly) have fixed the HG problem with them, or atleast cured most of it. But double check with some other guys on this site before takin my word.
~X=Remember, every problem is a blessing in disguise=X~
96 3.8 NA, 180* T-Stat, PnP Upper and Lower intake, Air Silencer Removed 9" K&N added to fender well, Mild J-modded transmission, 24K B&M Supercooler, 2.25" dual Magnaflow high-flow cats w/2.25" di/do Magnaflow, JVC El-Kameleon LX-30.
RIP Orion 800.4 amp, and Ascendant Audio 12" sub. Caught on fire in trunk...