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.
http://microdirect.co.uk/(13810)Gigabyte-GF-7600GS-Turbo-SLI-256MB-DDR2-PCIE.aspx
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.