If you're super lucky, it's just heatsink clogged with cat hair dust and other crap, basically overheating the card.
But that's rare... i'd bet it's probably something more complicated like some surface mount ceramic capacitors on the back of the pcb knocked off, and without those the gpu is unstable under load. Or some stuff in the power delivery is going bad once it gets hot.
As for power consumption, it has 2 pci-e 6 pin connectors so what do you think? The GTX 660TI cards peak at around 145w from 12v, so a 200w power supply won't be able to power it AND power a motherboard, a cpu and other things at same time.
Not worth buying anything with less than 4 GB VRAM these days.