Most PC hardware gives a thermal warning at 80C then shuts down at 83 or 85C to avoid damage.
It does indeed sound like you either have a bad or dying GPU perhaps even a failing cooling unit.
50C is a standard max load temp on effectively cooled systems.
Also most GPU's and games now run on 8GB VRAM and a minimum of 8GB system RAM (Recommended system ram is 16GB).
You may want to check your PC for dust buildup as this can greatly reduce heat dissipation.
You may be able to extend the life of your current system just by doing some routine cleaning.
I clean my PC tower out one a month.