The Debye theta for both KI and LiF had been measured over a wide range of temperatures, but as yet there was no clear indication that the theta as a function of T had leveled off. There was also no certain estimate of the value that theta would assume near T = 0. The present experiment was set up to find these values. Moreover, the findings were to be used to verify determinations of the theta by other means, and thereby help to tie together more tightly an extensive body of theory. Further, just such measurements as these are needed to shed light on recent attempts to extend the simple Debye theory.