A dual-mode, sapphire-loaded cavity (SLC) resonator has been designed and optimized with the aid of finite element software. The resonance frequency was designed to be near the frequency of a Cs atomic frequency standard. Experimental tests are shown to agree very well with calculations. The difference frequency of two differently polarized modes is shown to be a highly sensitive temperature sensor in the 50 to 80 K temperature range. We show that an oscillator based on this resonator has the potential to operate with fractional frequency instability below 10(-14) for measurement times of 1 to 100 seconds. This is sufficient to operate an atomic clock at the quantum projection noise limit.