I still don't like and it was where Star Trek started to lose the TOS fan base most hard or even soft didn't like the way he died not of heroics death.I would of lef it a mystery and revealed sometime later.They could always bring him back like Spock.
Age,
Kirk died a true hero's death.
He didn't die like a mythological figure- he died like a brave man. Because that was what he was... just a man. He got old, lost a lot of hair, chunked up, and (by the red in Kirks face) had a little trouble with the bottle. He was a brave man, but mortal man nonetheless.
If you leave it a mystery and reveal it later, you are still going to have the problem of how the man died; and one day you'll have to solve it.
And the 'bringing back' thing is FAR too overdone in Trek:
Scotty held in stasis.
Spock reborn on Genisis.
Worf dying during that spinal operation and Klingon genetics bringing him back.
Tasha Yar (my first moviestar crush, BTW) brought back as an ill-tempered Rom.
It's got to end SOMEWHERE... dead has got to be DEAD, or sooner or later it stops resembling reality. And that has always been a selling point of Trek- despite being fiction, it has always been at least marginally believable fiction.