[stareatgoats]

You are right, this tech would cause the core to lose temperature at a slightly higher rate than otherwise. At the moment the earths core is cooling at the rate of 0.1 °C per million years from the current temperature of about 5,100 °C, interspersed with periods where the temperature loss is stopped or reversed because of gravity forces [0]. But any conceivable number of deep geothermic wells would not affect that rate in any measurable way.

[0] https://en.wikipedia.org/wiki/Earth's_inner_core