60C even @500Mhz 0% load is way too hot, at idle desktop with one monitor @300Mhz I sit on 32-34C depending on the day.
500Mhz on the core clock occors when watching hardware excellerated videos (for example youtube), you can disable this by right click on the video and disabling hardware acceleration. Your core clock should sit at 300Mhz.
This sounds like a faulty card, RMA it.