An overheating GPU would most commonly play fine for a few seconds/minutes, then performance will decrease substantially as temperatures increase to unsafe levels. Most GPU's have thermal protection capabilities which would slow their performance down in order to reduce the amount of heat generated. In theory this will not cause a system to become unstable, unless the GPU is unable to reduce its speed and voltage to a point where the system will continue running. Such an issue could be a clear sign that the GPU cooling has an issue, be it heatsink mount related, or fan speed related, or perhaps it is simply clogged with dust and grime.
The clear cut answer as everyone else has mentioned, would be to monitor CPU/GPU temperatures, if...