Angus MacSpon wrote...

 It's established pretty explicitly in LOTR that the Ring doesn't really
 react to heat.  It WOULDN'T feel hot when he picked it up.

The Ring DOES react to heat; it just takes a lot more than for a ordinary
ring. When it was cut from Saurons hand, Isildur noted that it was hot to the
touch.
  

 (Unless that fireball was really SOMETHING, of course.)
 

Well, exactly. Lina's fireball is pretty hot (it melts iron) so it would
probably heat the Ring sufficiently to give Gourry an "Oowie."

-Mercutio
"A plague 'a both your houses!"