There are no LCD displays that I'm aware of that have fans. If your Sony is an LCD, then that's the first I've ever heard of a fan in an LCD---or even in a older CRT.
Apple monitors hot? If you want to know what hot is, run a large CRT. That will turn a small room into an oven in no time flat. The heat output of the Apple LCDs (I have a 20") is no greater than any other LCD out there. Even if it is, it's not worth worrying about as the light-bulb illuminating your room puts out more.
LCDs are much more energy efficient than the technology they replaced (CRT).
And, this is a topic better suited in the Image Processing forum:
http://luminous-landscape.com/forum/index.php?showforum=5