If the noise changes when the framerate changes, then it's most likely coil whine, not the fan. If you could describe the noise, that would be helpful. If it's a high-pitched whine / buzzing, sort of like an old tube TV, then it's coil whine.
On your graphics card, near the voltage regulator, are small coils of copper wire. Under certain circumstances, they vibrate at just the right frequency that you can hear them. It can be quite loud, depending on the card and how many coils it has and how they're made.
Coil whine is irritating, but normal. It's not a sign of a defect. Although I've never done it, I've heard that putting some tape or hot-glue on the coils will stop them from vibrating as much and will reduce or eliminate the sound. Keep in mind that this might damage your card and could void the warranty. You may also have to take off the large cooling shroud, which isn't always an easy task.
You could contact the manufacturer and ask for a replacement. They may not help you though, since it's not technically a defect.
It could be overheating for sure. Is the noise before or after the frame rate drop? If before, possibly overheating. If after, maybe your power supply is inadequate.
What kind of a noise? Could just be the fan spinning quickly. I would advise checking there are no loose wires being knocked by the fan, this could make a loud noise.
What Rich Barfoot said is correct. You can try and install SpeedFan. It's a program that shows you how hot stuff in your computer is. On my computer it lists my graphic card simply as "GPU". Try and run a game, then minimize it and open Speedfan. Your GPU should be at a max of about 60 degrees (~160 F). If it's too high it might indicate that the fan on the card isn't sufficient.
One solution could be to install a new fan on the card. It could also be that there's not enough airflow in your computer, so the air inside the box gets warmed up because it's not escaping. A professional should be able to help you with this.
if it is doing a clicking or scratching noise then it is broken , if you just hear it speeding up, then thats cause your video card is getting heat from the video game that is running , try lowering your graphics in-game , it might help.
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Your computer disk space is running low perhaps, and this causes it to overheat. Defragging can help you, (there is an option under the start bar if you're on windows)
1. Defragmentation would do nothing increase free disk space, so recommending it to someone who is low on disk space doesn't make any sense at all.
2. Defragmentation is much less effective on a disk that is nearly full. Sometimes, if the disk is full enough, defragmentation will fail because there is insufficient room to move the files around.
3. Disk space and fragmentation of the disk's contents have absolutely nothing to do with the graphics card or heat levels.
I understand that you're trying to be helpful, but please stick to what you are knowledgable about.