Temperature sensor using piezoelectric resonator and methods of measuring temperature

A system for measuring temperature, comprising:

• at least one piezoelectric resonator positioned in a subsurface borehole;
• a signal generator configured to generate an input signal and to vary a frequency of the input signal over a range of input frequencies;
• a receiver;
• and
• an electromagnetic waveguide at least partially positioned in the subsurface borehole, the electromagnetic waveguide configured to transmit the input signal from the signal generator to the at least one piezoelectric resonator to resonate the piezoelectric resonator and configured to transmit an electrical impedance of the at least one piezoelectric resonator to the receiver,
• wherein a minimum electrical impedance of the piezoelectric resonator corresponds to a resonance frequency of the piezoelectric resonator,
• wherein the resonance frequency of the piezoelectric resonator changes according to a change in the temperature in the subsurface borehole, and
• wherein the resonance frequency of the piezoelectric resonator corresponds to the temperature in the subsurface borehole.