  This paper brings out results of a measurement campaign aiming to determine
the temperature coefficients of synthetic quartz elastic constants at liquid
helium temperature. The method is based on the relationship between the
resonance frequencies of a quartz acoustic cavity and the elastic constants of
the material. The temperature coefficients of the elastic constants are
extracted from experimental frequency-temperature data collected from a set of
resonators of various cut angles, because of the anisotropy of quartz, measured
on the very useful cryogenic range [4 K - 15 K]. The knowledge of these
temperature coefficients would allow to further design either quartz
temperature sensors or conversely frequency-temperature compensated quartz
cuts. With extremely low losses, lower than $10^{-9}$ for the best ones, key
applications of such devices are ultra-low loss mechanical systems used in many
research areas including frequency control and fundamental measurements. The
Eulerian formalism is used in this study to identify the temperature
coefficients.
