It could be poor design work.... perhaps they don't have much airflow out the back, which traps heat to the front?

Hard to say - I only have experience with 17" and 30" - which are night and day when it comes to heat production. I have taken apart many a monitor though (used to make my own projectors). There are usually 2 CCFLs - on the top and bottom or sides (not both) and they are the source of almost all of the heat - the other heat generation is from the driver board - they are usually located on the back though, behind the LCD (not at the bottom or anything).

My personal suggestion is to replace them with 17" monitors.

Worth mentioning: make sure the heat is not coming from your computers and warming the screens up a bit (in addition to the heat being generated from the screens). This might be unlikely though - you can touch the monitors and pretty much tell. But, 4 or 5 boxes giving off a small amount of heat each in a room with a small size and poor air circulation is a recipe for sweat - even if its not heating the monitors.

Check the power bricks or the labels on the monitors. How many watts do they consume?