Quote: "Can it really be blamed on the graphics card if it was performing just fine without any problems up until this one video?"
Depends what's involved in this rendering process. Also, maybe the chip's on its way out. Constant heating and cooling wears things out (well they say that but I'm posting from a machine running a single-core Celeron CPU, lol)
Quote: "Would there be a way to get my computer to use less power to avoid reaching high temperatures?"
Don't think so. If it was a tower with a video card I'd say just go and but a new Heatsink & Fan combo for it (there are some really cool ones available - bad joke) and add some case fans but with a laptop I dunno what to suggest.
"Quotes in signatures are just stupid, especially if you're quoting yourself" ~ me