I have the same display. I fixed the problem by buying a usb case fan and hooking it onto the back left (if you are looking at the back of monitor on the left) side of the monitor. Under the back left side of the monitor is a piece of plastic that can be removed to reveal a usb port, you'll need something small to pop the piece of plastic off. If you want to attach the fan as simply as possible, you could just bend a couple paper clips into hook and hang the fan in the grill like backside of the monitor. Plug it into the monitor's usb port and you're good to go. Fan will only power on when monitor is on and black screens will be no more.
Sounds legit but I called em since it was under warranty, they said power issue. Called Wensday, got the box Thursday, sent it Friday and got it on Monday. Sony actually did something right, giving u the best answer tho, cuz u put in so much work