HP ZR2740w keeps going dark

Question

I recently purchased an HP ZR2740w monitor from B&H.  I had hoped to use it as a second monitor on my mac mini, but it pretty much flat out won't work on the mini other than at something like 1280x724, much worse than my Dell 1920x1080.
It would work, quite well for a while, with my Linux box through the display port, showing full resolution.  I'm running Linux Mint 17 (Qiana) on and Asus Z87 plus mother board.  I have three display set up, a Samsung SyncMaster 213T running via an hdmi->dvi adapter at 1600x1200, the HP on the mini display and a ViewSonic on the VGA.
The problem is that after a while, the HP will go dark. like it is in some power saving mode. Even if I'm playing a video on it.  It still tells the computer that it is there though, as my windows stay on the dark display and don't move to other displays, like they do when I turn it off. Also my cursor has to traverse the space of the dark display in the middle.  
Once it happens once, I can sometimes bring it back by hitting the power button, but the next shutdown is much quicker. Somtimes, hitting the powerbutton will only show an image for less than a second before darkenss, in which case I have to cycle the power with the hard power switch on the back.  
It seems as if this monitor has some sort of "sleep mode" to save power, rather than letting the computer decide when to do so.  The other possiblity, since the up times get a lot shorter, is that it is overheating and automatically shutting down because of that, but I can't imagine an LCD overheating in regular usage.

Answer 1

My comment about it being heat related prompted me to try to turn down the brightness, it being the only control on the monitor.  Without any sort of objective brightness indicator on the display (Why did you remove the OSD menu anyways?) it wasn't immediately obvious that the button was having any effect.  I did, however turn it down until it was visibly dimmer and have been playing video continuously for about an hour and a half without the screen blanking on me.
So, if the display has an overtemp cutoff, I may have figured out the solution.  If the display is not supposed to have an overtemp cutoff, then this one seems to have a temperature dependent fault.