The fan will depend on how hard you drive the monitor. If you use sensible brightness, dark desktop setting, avoid very bright wallpapers, don't leave very white items on the screen for long then all of those things keep the panel cooler. In turn they also help avoid burn-in.
My PC is silent when idle, so it could be a distraction, but I am not getting rid of my old monitor. The new one will be off for everything except for the thing it was designed for - games! During games it can make as much noise as it likes, because the speakers will be making more!