Dead graphics card for certain. Funky colors and screen artifacts are a definite symptom. Graphics cards can run boiling hot literally (> 100C) but that should only be under load.
They can get very hot to touch (~60C) even at idle. If the heatsink isn't exposed, try taking the shroud (metal cover) off the card. A dust clogged heatsink will cause those kind of overheating shutdowns.
It's very likely that a cooled card will behave (or it could be burnt out permanently).
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