GT610 is the lowest-end card of the series (evident by the #1 in the model name, the #6 is the generation name), which means upgrade options for the card are extremely scarce and/or non-existent.  Most users of such cards might actually go through the hassle of returning the graphics card (and sometimes the whole computer tower it came with) if the noise is really bad.
 
That said, you could just unplug the tiny 2-pin power cable that fan motor is attached to the card and try it out without the fan running but still attached in case it is needed.  The GT610 card itself barely sips 30W of power for the GPU and the memory and other circuitry, it might not overheat that quickly as long as your computer has additional fans that circulate air inside the case.
 
FYI, you will be told by someone that GT610 isn't a gaming card; please ignore them.  It isn't that they are wrong, it is just that many frequent visitors to this website own high-end (model names with #7 or higher) and think the only way to play a game is the with details turned up, which is only fluid and smooth with the most expensive stuff (which is BTW, the status quo around here).  They forget that not everyone shares the same preferences, maybe you don't need so much "pretty" just to play a game, or that you wouldn't pay so much for it.
 
Bottomline, don't take opinions for face value; if it isn't factual, there is a lot of bias.

I also have the GT 610 2GB, it does punch some noise but not bothersome actually. The card plays all the latest games that are out today. With some games, you may need set it either on medium or low. But as of now, I haven't played any video games with the settings on low. I was surprise when I seen Crysis 3 played and zero lag on high settings. Just have to turn off the anisotropic filtering in the latest games and it will run on high settings.

 
So yes! What Lehpron said up there is true. Those who uses the GTX cards thinks to play Battlefield 3,4 or Call of Duty Ghost you need a GTX card. You can add a little juice to your GT 610 using the EVGA Precision X. I have it currently overclocked at 860MHz for the GPU Clock, and 562MHz for the Memory Clock. It wont add much speed to the card, but you wont be disappointed either when see the result in gaming =)

Actually I think you missed the point of me pointing out the GT 610 can do more than what many never looked upon.