Power supply fan noise only when computer gets hot. Why??

the computer monitors power/heat usage and just turns the fan on...it's a good thing... if you can't stand the fan, clean the dust out or replace it with a brand new one.

Look very carefully in the area of the fanS and ensure there are no wires routed such that when the fan speeds up they are pulled into the blades by the airflow.
Also look for wires or something else (tail of a zip-tie, tail of a tape wrap) that is close enough to the airflow to be caused to flap or vibrate.
.

Depending on how it's mounted the entire fan may be vibrating in it's mount. (Clipped in vs screwed down.)
.

I think you'll have to try to explain the clicking sound better. As has been suggested, the fan often runs faster when things get hotter, but that shouldn't make a clicking sound, but rather just make the noise louder. Maybe there is a thermostat that is turning on or off, that would cause clicks, also a relay which controls the fan to turn on or off would be audible. But without really knowing how that clicking sounds and in what cadence it is happening, it is difficult to tell what the cause is.

Might want to better define what is making the sound.  VERY Carefully unplug your addon fan and power up the system just long enough to hear the clicking or when you would normally hear the clicking noise.  If heard then not you addon fan, otherwise it is your addon fan.  
If your Power Supply Fan then check for "anything" that might be pulled into the fan blades.  Also, might check if the grill covering the fan(s) can be adjusted/bent Very slightly or a Very slight spacer can be put between the grill and the fan.  Be sure everything is tightly secured.
Then again if your system is under warranty let the warranty take care of this problem.  (Warranty Service, Replace any clicking part, etc...)  

Hope this Helps!!!

Ooops, most of my above is just a recap of previous comments with only the suggested actions or action variations that might be unique.  :-)

You said that this only happens when you play graphic intensive games.  Does your Video Card have a fan on it?  It may be that the video card fan is kicking in to cool the Chip.  If that is the case, check to make sure there are no wires or other items near the fan on the Video card.

Mav

Thanks for all the replies!  

mav7469 - it's definitely not my graphics cards since they are near the bottom of the computer.  Yes, this only happens when I play graphic/CPU intensive games.  While the game is running, I actually listened to where the sound is coming from and it's definitely coming from the top rear of the computer case, where the power supply is.

I will take the advice here from all of you and take out the power supply and check if there's any loose ends hitting the fan in the power supply.  I don't really know how to check this out since I don't know too much about how to take out a power supply and check it out, and plus there's no warrantee or anything.  

One additional thing is that when my computer is not making that noise and is at idle, one time I accidentally bumped my computer with my leg and I could hear that "clicking" sound coming from the power supply again, but the clicking sound happends once, not continuously.  So, I purposely bumped it again gently and sure enough that sound is heard, but only once.  So it seems like there's a loose part in the power supply?  I don't understand, but I'm going to take out the power supply anyways and check it out.

Any advice to properly and safely take out a power supply?  Thanks again for all your replies.

At a high load the power supply may loose energy due to the high power transfer through the chopper.
This can be done by electric arcs that hopefully be seen in the dark. Try and look for them inside the power box.
If that is the problem i think the PS is too old and need to be replaced by one more powerful.

It's simple to take out the PS, you just need to remember the location of the screws and move it gently. Normally thee are 4 screws for the caver and 4 for the fan if you need. First unplug the power cord. If you change the PS unplug all connectors of course.

Make total dark and power so detached, with all the cables connected again, only if it's possible. Load the system and wait to make noise. See any flashes? If yes locate them and tell me where they are.
After this test, exhaust the dust inside the PS and repeat the test.

I forgot something.
Before doing that complicated things that i said above lets test the PS fan. Don't take off anything yet.
Take a bamboo toothpick and insert it slowly antil touch the fan blades to stop them temporarly. Wait until that sound show up and after that stop the fan. Move the case, make it appear, do you hear it again?

Is simple.
Unplug it.
Disconnect the wires.
Remove it from the case. (Usually 4 mounting screws.)
After this you just need to look and figure it out. Is not hard..
Usually the PSU cases are two halves held together with a few screws.
Usually all the components are mounted on one half and the other is just a cover.
You know the kind of thing you are looking for in there so good luck..
.
There's a pic here:
http://computer.howstuffworks.com/power-supply.htm
.

you can use a quiet power supply, and a quiet heatsink to eliminate the noise lowest heat transfer resistance !

http://www.zalman.co.kr/eng/product/code_list.asp?code=009

http://www.zalman.co.kr/eng/product/view.asp?idx=194&code=015

Thanks for Points friend  !!

Maheen