References

Measurement of Heat Capacity

Denlinger et. al., Rev. Sci. Instrum. 65, 946 (1994). This is our paper.
Stewart et. al., Rev. Sci. Instrum. 54, 1 (1983). Provides a neat overview of the measurement of low-temperature specific heat, including motivation, history, and special problems encountered.
Bachmann et. al., Rev. Sci. Instrum. 43, 205 (1972). An early version of the relaxation method that we employ, applicable to bulk samples (not thin films).
Sullivan and Seidel, Phys. Rev. 173, 679 (1968). The ac method.
Graebner, Rev. Sci. Instrum. 60, 1123 (1989). A clever method for milligram samples mounted directly on a thermocouple.
Geer et. al., Rev. Sci. Instrum. 62, 415 (1991). Graebner's method applied to liquid crystals.
Early et. al., Physica B 107, 327 (1981). Some of the first work on thin-film calorimeters, using a sapphire substrate and the relaxation method of Bachmann. They use boron-doped epitaxial silicon thermometers, the precursors to our B-doped poly-Si thermometers. In fact, this is work done by my thesis advisor, Dr. Frances Hellman, while she was a graduate student at Stanford.
Kenny and Richards, "AC Calorimeter for measurements of adsorbed gases on metal films at 4He temperatures", Rev. Sci. Instrum. 61, 822 (1990). Another sapphire substrate, used to measure very small quantities of material (as small as a few tens of monolayers of helium) at low temperatures. They use an ac method similar to that of Sullivan and Seidel.

General Solid-State Physics Textbooks

Ashcroft and Mermin, Solid State Physics, W.B. Saunders Company, Philadelphia, 1976. I recommend this book most highly because I really think it's the best. Clear, fairly concise, and covers everything you need to know.
If you must have another, try Kittel, Introduction to Solid State Physics. He covers all the basics, but over the years he has been (in my opinion) rather sloppy about revising. New sections are added almost as non-sequiturs, with inadequate fleshing-out of the text. The result is a book that is readable only if you already know the material.
There's one by Ibach and Luth which is also pretty good because it contains some really nice descriptions of real-world experiments. In general, it has more of a "practical" focus than many other such texts.
If "practical" makes you wince, try the two-volume series called "Solid State Physics" by .... (a couple of theorists; I'll look it up and add it if I remember). These two tomes make great bookends, or you can read them and try to wade through the piles of indexes, overly florid equations, and dense text. (To be fair, I've gotten a couple of useful things from these, but really, they're for theorists).
There is also a book by Ziman. I don't know much about it.

A book that all scientists and science fans must read:

The Character of Physical Law by Richard Feynman. (MIT Press, Cambridge MA, 1965).

This slim little book is a gem. Feynman eloquently describes the relation of mathematics to physics, the role of symmetry in the laws of nature, the nonintuitive qualities of probability and quantum theory-- all in everyday language that anyone can read. Feynman celebrates the beauty of the Universe we find ourselves in, and delights in our gamely quest to understand its fundamental properties. He sees physics as separate from mathematics; math is just the "language" we use to describe it. His understanding of Nature is deep, and his enthusiasm contagious.

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