Thank you very much for your advice, everyone! I really appreciate it.

I decided to do an experiment with the game last night to see how the fans react. I've noticed that my fans always become louder when I spend an extended period of time in Gridania and/or The Black Shroud. So, last night, I decided to play Final Fantasy XIV as normal with one exception; do not enter The Black Shroud nor Gridania. The result was quite unexpected; the fans acted almost as quietly as when I'm not playing a game! I suppose this means I should avoid those areas until Square Enix optimizes the game, or at least until The Black Shroud gets a redesign. All client crashes that ever happened to me in the game ever since I got this PC was in Gridania anyway. (That place is cursed, I swear it!)

Once again, thank you everyone for your help, and good luck to you in your current and future endeavors.