Screen goes black when hot

Hi guys, I’m having an issue with my 2013mbp. The screen goes black whenever it starts running hot at the slightest. I’ve been battling with this issue for months now. The two times I changed the thermal paste, it worked for few days and goes back to that problem of black screen while the fan is still running and keyboard still on sometimes.

Recently, the screen doesn’t even come on again, it’s just the fan alone running.

Could this be an issue from the heat sink? I don’t mind replacing the heat sink. Someone should please help me with what the problem could be and possible solution. I spent my last money buying this laptop and now I’m faced with this issue.