There are two steel clips on each side. The easiest way I have figured out how to do is is remove the whole cup holder assembly and then use your fingers to push in on the two metal tabs that hold the unit in, but you have to bend your finger up and push into the unit. Ha its a little hard to explain.
The clips are about the same thing that hold the dazzle/turn signal lights into the rear bumper if that makes sense.
You can barely see the metal clips in the attached picture.
Finally got around to taking care of this... everything above is correct. My dealer didn't even have this bulb, so ordered it from AB. Here is some detail for those worried about this minor operation:
#2 Phillips screwdriver (magnetic tip would be great)
#1 Phillips screwdriver
one or two flathead screwdrivers
Remove the coin and ash trays. Remove 3 x Phillips screws on each side (6 total) of temperature unit; these hold the entire plastic assembly in place. Set assembly aside. On the right side of the unit, slide a couple of fingers in the opening and feel for the smooth steel spring plate. Depress and at the same time take a flathead screwdriver and prise the edge of the unit out a few millimetres. On the left side, the push-button controls make it a little harder to access - I pushed the closest two to the temp. unit out a little - you can just give them a nudge from behind. It isn't necessary to pop them all the way out. My fingers aren't very flexible, so I used a second flathead screwdriver to depress the spring plate on this side, while using the other to pry out the edge.
Once released from the dash, depress the release button on each of the three electronic connectors and remove. I had to give them a bit of help with a flathead screwdriver to get them all out. Place the temp. unit on a flat surface and remove the two small Phillips screws. Gently separate the unit - the ribbon cable is quite thin - it is not necessary to unplug it. The defective bulb can be removed with a simple twist or quarter turn from a flathead screwdriver. Install your new bulb, and reverse the procedure to put everything back together.
An old thread but in case anyone does a search, I'd like to add this. I removed the unit today and I think that the easiest way I found to remove the climate unit is to remove the switch cluster on the left and the lock/clock cluster on the right. These are relatively easy to do: for each one, side two credit cards, wide-side in, one at the top and one at the bottom, far enough to release the clips (two on top and two on bottom). The cluster will then slide out readily. With these out, it's simple to reach in with a finger on each side and release the metal clip holding the climate unit in place, and just pop it out. Atlantic British has a video suggesting sliding screwdrivers into the side of the climate unit to release the tabs, but I'm pretty sure that'll chew up the plastic.