But realistically, you're probably OK. Years ago it was not at all uncommon for people to throw their then-new polypropylene underwear into the dryer, only to pull out a small ball of compacted, hardened fabric 45 minutes later. I suspect that's what your "What-were-you-thinking?" friends are likely remembering. These days, better fabric technology ensures that most outdoor garments are actually quite washer/dryer-durable. Manufacturers such as Marmot, in fact, have rooms full of washing machines and dryers, testing all their garments in real-world cleaning conditions. The fact is, warm drying even helps Gore-Tex a little, because it softens and re-spreads the durable water-repellent (DWR) coating, helping better protect the fabric against wetting out.
That said, a little caution never hurts. The general rule of thumb for washing and drying Gore-Tex jackets is as follows: Machine-wash on normal setting with warm water, using a bleach-free detergent. Certain liquid detergents used to have emulsifiers that could damage DWR. This is supposedly no longer the case, so powder or liquid detergents are generally fine. Then, dry the jacket on a low or medium setting. It won't hurt to throw in a few cotton towels if the jacket is by itself; the towels will speed the drying process and act as a thermal buffer if the dryer does indeed get very warm. Do that, and I don't think you should run into any problems.