Are you sure its the graphics card?
In answer to your question "Which Fanless graphics card?"
I would go for a Gigabyte 7600GS which is in line with the price of the one you showed. And this one truely is fanless not like the one from Aria.
However, what have you done to be 100% sure that the cause of your system restarts is your current graphics card? The restarts of your system shouldnt happen at all. I can play games for endless hours or video editing without it crashing/restarting etc...
Have you made sure its not the CPU overheating, bad memory, PSU voltage issue, bad sectors on the hard disk etc... I wouldn't spend any money 'til you know exactly what the cause of the problem is. Your current graphics card could be fine.