when heated (above, say, 600
oC) Silicon dioxide increases its ( verylimited) conductivity. Think in the order of about 10
-10 - 10
-6 Ohm
-1.cm
-1.

Srivastava
et al., J. Electrochem. Soc. Vol. 132, No. 4 (1985) p. 955
At room temperature of course it is an insulator (glass)
The authors of this paper attribute the higher conductivity at high temperatures to contributions of ionic conductivity. Basically, they say the oxygen atoms (ions) can move around in the material at such high temperatures and generate charge movement (conductivity) that way. (they also discuss the effect of support --in their case p or n-doped silicon--, which can help create oxygen vacancies and increase conductivity as well.)
So not so much the influence of silicon as the influence of oxygen!