I dont even know where to begin with the poor advice being given here...
The harder the GPU works the more the fans have to spin up to keep the card cooled off. This is pretty normal. Some cards have louder fans than others, but reviewers don't always note that in reviews.
To remedy this:
You could get a liquid cooling setup (expensive and not really for novices to build or replace).
You can try to find a similarly spec'd video card with a passive cooling system that might (or might not) work in your PC depending on the layout of your case and how well it is cooled overall.
You can get a utility to control the speed of your fan directly, but this is also not for novices.
You could put the PC on the floor. The sound from fans doesn't travel that far.
You could get some sound-proofing material for your case. Typically this does not make the big difference that manufacturers claim / imply.
Or..
The easiest and cheapest thing for you to do (aside from moving the PC) would probably be to wear over ear headphones.
1. Skip Liquid Cooling. Unless you want to pay for professional installation, it is not something anyone can do. You need to know what you are doing and it is very expensive.
2. Any passive cooling version of the card will require toning down settings a lot. Passive coolers are not as good as active ones, so it is required that you already have great airflow in your case.
3. Not suggested. If the fan is speeding up, it means the card is working and is thus producing a lot of heat. Toning down the fan is dangerous as you might fry the card.
4. That is a valid option. Also a blanket over the case can help dampen the sound. Just be careful not to cover any vents or intakes for the fans.
5. Not worth it.
Do you have airflow in your case? If your case is locked up tight and it turns into a heat box, maybe opening the case a bit to get some air movement would make it cooler, take your case off and then try it for a bit.
Case off is a louder fan, but if its cooler, it won't spin as much.
If you do get a utility to tweak the fan, play with the speed settings in 1% increments and you can find a right fan tone that can match your power supply fan or any other fans and helps to turn it into white noise, when its fluctuating is when it gets noticeable.
Opening the case is not the best idea. Cases are designed for create a wind tunnel by drawing in air in the front, and releasing in the back. Opening the case disrupts this flow of air and can actually increase the risk of something frying.
And again, messing with the speed of a fan is not advised. If it is simply for sound control, you are risking overheating and burning out your video card.
Would this be a good (more silent) card for F3 and FNV?
http://www.salland.eu/product/304238/gigabyte-geforce-9800-gt-1024-mb-gv-n98tsl-1gi.html
http://www.pcarena.pl/uploads/images/XFX_GeForce_9800_GT_01.jpg
Core click is a little lower (600 mhz) than my current 625 mhz, will this be a problem with NV?
Nearly all 9800 cards have the same fan. Any alternative you may get is just a waste of money.
The core speed is moot. Little difference between a 600 and 625 MHz core. It if were something like 600 vs 670 or 700, then yes, that would be better.
But if I'd have the money to update my card, that'd be best?
Depends. If the rest of your computer is up to par, then there isn't really much of a downside. If not, then you are throwing money away by causing your new card to under-perform and can actually hold your entire system back.
The most efficient computer isn't the one that has all the best parts.