I vaguely recall (from 30 years ago) doing temperature runs of various
crystals in a fixture. While we were primarily interested in their
frequency versus temp characteristic, I also recorded the series
resistance. The series resistance varied wildly over the production
lots received from the vendors, but each crystal was fairly stable
over temperature. I vaguely recall that it was almost linear, with a
slight decrease in series resistance with increasing temperature.
The normal quartz processing includes some water-cooled
grinding and polishing; it turns out that OH radical contamination
can dominate the internal losses. The effect, as I recall,
is minimized at elevated temperature (80 C or so?).
I dimly remember Hughes corporation was involved in making
artificial quartz crystals, and found that growth
in water caused the artificial quartz to be inferior to natural.
Alas, this was 20 years ago, it'd take a search for 'alpha SiO2'
in a good library to find a reference.