Cold Cathode/LED Lights

I'm going to place a glass corner shelf above my bed for odds and ends, but being that it is somewhat small, I want to save the space that putting a lamp there would take. In lieu of the lamp, I'm considering putting either a cold cathode tube or possible a LED light inside of the mounting bracket, which would require that I drill some hole in the lower portion for the light to shine out.

The area in which the lights would have to fit is an isosceles triangle measuring 1"x3/4"x3/4". so I think that it will fit. the shelf is this one"

12" X 12" KV Clear Glass Corner Shelf Kit w/ Black Brac - eBay (item 260692297911 end time Mar-13-11 09:58:48 PDT)

It is not apparent in the photo, but it has a couple of plastic endcaps to seal the ends. However, since this would create a small closed environment, I'm wondering if the heat buildup would be something to be concerned about?

EDIT: Also whether 8 1/4" holes on each bracket would cause the light to spread, like it does with plexiglass? This shelf is tempered glass.

Hi seekermeister :), On my computer desk I have a lamp that is 10 LEDs and after being on for hours there is very very little heat buildup (placing my hand on the clear perspex its a lot cooler them my monitor screen) using LEDs you will have no problem ... and they come in many colours.

Info Light Emitting Diodes (LEDs)

Hmm, those won't work the way that I want, because they are DC, rather than AC like I want. Can't see any reason to worry about batteries when there is an AC outlet a few feet away.

My lamp is AC and does not get even warm.