Firstly … don’t run your machine without the fan working 100% … you could end up cooking your GPU and permanently damage it.
The quickest fix is to remove the card and try to check the fan for dust and debris … see if you can remove it if it is there. Try to find a blower or a vacuum cleaner that has a blow option or a air compressor and blow the fans clean.
If the fans can be unscrewed … remove them and check the underneath for dust and debris and stuck in the back.
Finally you can try some Silicon Spray (like WD40 or Q20) and spray that between the housing of the fan and the part that spins … this normally does the trick. Spin the fan by hand first to remove excess silicon spray and then dry the overflow.
If that doesn’t work then chances are the fan has gone … check the fan’s power connections and the card’s power connections that they are seated properly. Sometimes they come loose.
You can also try finding a suitable replacement fan from a computer components shop or similar shop (Radio Shack, A1 Radios) and try to replace the fan.