We carried out measurements of thermal conductivity in a crystal quartz substrate (900 (micro)m thick) at temperatures of 1.4 K by using a pumped ^4He cryostat. We applied a varied imput power from 0.1 up to 1 mW to the heater placed at the end of the substrate, and we observed that the measured data give a temperature dependence of k=0.127^2.7 W/cm x K.
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