It's attached to the plastic border of the monitor, and it only gets just warm.
But... I'm probably phrasing myself poorly.
These lamps they emit heat the same way as light, in a cone away from the lamp. So even though the clamp attached to the monitor is not getting hot my concern is that since part of it is shining at the monitor will that damage the screen.
For example, if I put my hand right in front of the lamp (not touching it) it gets uncomfortably hot pretty quickly.