Try and isolate that is directly the card that's the problem and not other factors on your machine. This may be tricky by try using that card on another known good machine to see if you experience the same thing.
If you do, then that should be enough to convince you it's a problem with the card.
At the same time you could test another graphics card that should be working well on your machine, and if you have no issues with the alternate card then you should have confidence in the rest of your system configuration.
As for software, try a variety of graphics benchmarking software to put the card through some of its paces, along with something like RealTemp or GPUTemp as an indicator of how warm its getting under load.