The glass transition temperature of quartz is 1200°C, and according to the charts I could find, is outside crust and upper mantle temperature ranges. (That is just based on averages, I believe. Heat from friction may be in a different category.)
Edit: The melting temperature is ~1700°C. It probably starts to get malleable around 1200°C. I was confused about the term “glass transition” due to some of my hobbies and likely does not apply.
Other silicon-type rocks (like gypsum; opposed to quartz) have wildly different glass transition temperatures in the 200°C range. That seems feasible to bend in a lab and could be in-scope.