I have a 24 in. flourescent fixture, single tube, open design with no lens or shade. UL listed for dry locations only.

Is it safe to mount this fixture to the bottom of a wooden shelf (in my utility room)?

This would put the side of the fixture that has the ballast mounted to it right against the shelf. My concern is the note inside the fixture that states that supply wires located within three inches of the ballast must be rated for 90 degrees C. In my experience, ballasts become quite warm, even hot.

Are these fixtures designed to be mounted to surfaces, or only to be hung by chains?

Real good question! I hang them on other surfaces direct, like sheet-rock all the time. Don't think I have ever done one direct to wood.... Wait, I have hung them direct to framing, and all of the undercab's I put up are all direct to cab's. I don't remember ever seeing something that says you can't.

For anything electric, UL's tests include some sort of overload/short circuit test, during which the enclosure is monitored for temperature. The temperature, in genreal, is not allowed to exceed a value that they associate with being likely to ignite easily-ignitable materials, such as wood or paper.

There are exceptions; for example, we have all seen fixtures marked as not being suitable for use inside dwellings. This marking is there because, in the absence of free air flow, these fixtures do get too hot for fire safety.

As for the insulation requirements, the UL tests also include some sort of environmental testing, which may include running at a higher than normal temperature for an extended period of time. The higher-rated insulation is required to protect against premature breakdown of the insulation over time. This has nothing to do with failure effects; quite often, a failure (such as a bad ballast) will get hot enough to damage even specified wiring, and some length will have to be replaced.

Unless the fixture's directions, or marking, prohibit directly mounting the fixture against the ceiling, there should be no problem mounting them to a wood shelf.
Even at 90 degrees (centigrade), wood is in no danger of being burned, charred, or ignited.

That fixture should have dimples on it that give the fixture about a 1/4 inch air space when mounted.

That's no problem. All the older style undercounter lights had full size ballasts. Modern store shelf lighting can also be mounted directly to wood.

There are dimples on the mounting surface, but they protrude maybe 1/8 or 1/16 inch.

Thanks, I feel safer now after reading the replies.

BP