Yes, and sometimes suspension of disbelief is stretched tight enough to snap, and "it's fiction" is a poor excuse.
I didn't check UMN specifically; a 10-second Google for "hypothermia survival in water" produced the handily titled "Hypothermia Prevention: Survival in Cold Water" page near the top of the results. Other pages agree with their time-line for exposure to freezing water of <15 minutes = unconscious, 45 minutes = dead.
As for overall timing, the fic specifically mentions that Spock has been flat-out running for 28 minutes before he finds Jim. Allowing a bare couple of minutes to dump Sulu and Chekov in the cave and head out, Kirk has been soaking in freezing water for at least half an hour before he is found. The man has uncanny luck and mental talents, but he's not actually superhuman; he should at least be unconscious by the time Spock gets there.
no subject
I didn't check UMN specifically; a 10-second Google for "hypothermia survival in water" produced the handily titled "Hypothermia Prevention: Survival in Cold Water" page near the top of the results. Other pages agree with their time-line for exposure to freezing water of <15 minutes = unconscious, 45 minutes = dead.
As for overall timing, the fic specifically mentions that Spock has been flat-out running for 28 minutes before he finds Jim. Allowing a bare couple of minutes to dump Sulu and Chekov in the cave and head out, Kirk has been soaking in freezing water for at least half an hour before he is found. The man has uncanny luck and mental talents, but he's not actually superhuman; he should at least be unconscious by the time Spock gets there.