Video card causing system crashes?

Recently my PC has been shutting down during games. The error report I'm receiving is "Blue screen error caused by a device or driver" (the specific cause wasn't given). I have a Radeon x1950 Pro, I forget how long I've had it but definitely no more than 3 years. I have updated the drivers but that had no effect.

Depending on the game, the error occurs within minutes but it can hold up for an hour or more. Today I was using AtiTool (although my card isn't overclocked) and on two occasions the system shut down as the GPU temperature reached 70 Celsius, so I think it's an overheating problem.

I took the card out and removed as much of the fluff and dust as I could, but this made no difference. So I took the heat-sink/fan off and found that the thermal paste/pad (whatever comes with the card) looks to have worn away, so I've ordered some new paste.

From what I've described, could overheating causing my problems?