105°C is the max temp for most nvidia cards so that will explain the black screen. Have you cleaned the heat sink (cooler) on the card? It is worth a try before replacing it.
actually i cleaned it last month and the worker say the cooler didn't worked because the dust etc( it start around 1 and half month ago ) so after he cleaned at first i can play just around 1-2hours after that the same think happen maybe i will change with a new GPU this month i considering radeon 5770/5670(i need help for this too) and maybe add more fan
btw what is the normal temerature for GPU when we don't playing and when we're playing game?