Last week, several readers were pointing out stories of white iPhones that had taken on a yellowish hue. It was assumed that heat was the issue. Keen to tempt fate, I played Star Defense [App Store link] for 30 minutes straight last night with my iPhone resting on my bed. It warmed up pretty good, but stayed white.
Earlier today, frenchiPhone.com reported that the issue is most likely the combination of a hot iPhone and a certain case, though they did not specify which one. Additionally, they state that cleaning the effected area with a cloth and some rubbing alcohol will remove the stain. We haven't tried this, so we can't confirm that it works/won't damage your phone.
Our best advice, based on the limited information we have, is to remove your white iPhone from its case if you're going to be doing someting intensive for a long time, like play StarDefense, run a GPS app, etc.
I probably don't have to tell you this, but just in case ... do not apply stain stick to your iPhone.