Yeah if you're getting artifacts/lock ups and you're not overclocking, it is definitely the result of overheating. So the issue lies with one of these two things:
1) Poor air movement in your case (hanging cables, weak fans, lack of fans, etc).
2) Your video card failing to increase fan speed...
70C really isn't that bad, my old 8600GTS ran at ~85C at full usage. My current video card, which is a 450 GTS, runs at about ~55C. Though, your video card should not be crashing at those temperatures no matter the stress load, video cards are meant to get to >90C.
Also, are you overclocking...