Since we're trading horror stories...
My grandfather worked as a machinist for many years and got lots of small metal "splinters" in his eyes and never got them removed. This was back in the the days when men didn't wear protective gear.
Then one day he goes to get an MRI and they tell him that its going to be a problem and they're worried about the metal in his eyes. I guess the magnetic field in the MRI heats up the metal particles or something.
The problem with having metal in your eye and going to and MRI is that an MRI generates a massive electromagnetic field. You are right the metal will heat up and it will also cause the liquid in the eyeball to heat up as well which can change the shape of the eyeball due to the fact that your eye cannot release pressure. But another larger problem would be if the metal in his eye was of the type that is attracted to EMF's (I think only 3 types of metals are), the small splinters of metal can be forcefully pulled from the eyeball and cause all sorts of damage depending on the direction of travel when they try to connect with the magnet.
I know someone who works as a metal machinest and was refused an MRI because for the slight possibility that he could have very small amounts of metal in his lungs. I remembered him telling me the story and figured I'd pass along the MRI thing as your post just jared my memory.
Yup. As one who needs to get MRIs once a decade or so, I try to do as little metal work as I can.
And a one up on the horror stories:
(Warning: death in story)
A few years ago a metal oxygen gas tank was brought into the the room of an MRI machine and
was left there. (Nothing un-bolted down metalic item should be in the room during MRI operation.) When the machine started, the magnetic field was great enough to pull the tank up off the ground, into the machine, and halfway into the head of the kid having the MRI.
Luckily, this happens very rarely. Of course, they make you remove all jewelry and empty your pockets. If you wear any clothes with a zipper or metal buttons, you need to take it off and wear the hospital gown. (Sweats and a tshirt are recommended instead, at least by the hosital I go to.) Tooth cavity fillings are fine.

Which reminds me, time to schedule my next MRI. [shrug]