There are thermal protection systems in place to prevent something like that from happening, even if there was a fault somewhere causing a power spike or overheating. If one of those systems are activated, the computer would react just like it did in your case and shut down. When electrical components get really hot, they start smelling even if they aren't ruined.
High indoor temperature, bad airflow or dust buildup in the PC may be causes for overheating when doing performance intense tasks.
If it really is broken, there is almost certainly a fault in the hardware and your graphics card (or some other component) would have eventually failed regardless. I would definitely try booting the computer up and see if you get any video output rather than assuming the worst case and possibly wasting money on a new GPU.