Okay, here's my opinion:
Forostar said:
Warm metal features melodic singers where cold metal features less melodic singers, even shouters. In warm metal, with the music there's more emphasis on melody as well (and melodic guitar solos, and harmonies!), and in cold metal less. In cold metal (e.g. trash) it's more about riffs, and aggression.
I think that this is a good definition, but I can't say "THRASH METAL IS COLD" because every band is different. Both Metallica and Megadeth play thrash metal, but IMO Metallica is cold, and Megadeth is warm. Both Stratovarius and Blind Guardian play power metal, but Stratovarius is cold and Blind Guardian is warm.
About your power metal definition: it's good, but I think that you're only referring to European power metal.
IMO there are 3 sub-genres of power metal:
-US Power Metal (bands do not have to be from USA to play US Power Metal, but they mostly are)
Bands that played fast and melodic dark thrash/heavy metal with clean high-pitched vocals in Dickinson/Halford style. First bands that come to my mind are Jag Panzer, Helstar, Angel Dust (although they are from Germany; 2nd album), Iced Earth (first 2-3 albums), Manowar, Megadeth (some songs), Anthrax (albums with Neil Turbin), Agent Steel, Crimson Glory (first 2 albums) etc. Judas Priest's Painkiller could also be counted as a US Power Metal album, although Judas Priest are from England.
-European Power Metal is mostly happy, melodic, more anthemic than US Power Metal, features fantasy cheesy lyrics and more prominent keyboards. Bands: Helloween, Gamma Ray, Stratovarius, Sonata Arctica, Masterplan, Edguy, Avantasia, Sabaton, DragonForce, Nightwish etc.
The third group features bands that combine power metal with other genres, like Children Of The Bodom (with melodic death metal), Ensiferum (with melodic death/folk metal), Kiuas (lots of other genres), Symphony X (with progressive metal) and lots of other bands.
I also consider that some Iron Maiden songs are power metal, especially the ones from Somewhere In Time and Seventh Son Of A Seventh Son - songs like Caught Somewhere In Time, The Loneliness Of The Long Distance Runner, Moonchild, Seventh Son Of A Seventh Son...