  We demonstrate thermometry with a resolution of 80 $\mathrm{nK} /
\sqrt{\mathrm{Hz}}$ using an isotropic crystalline whispering-gallery mode
resonator based on a dichroic dual-mode technique. We simultaneously excite two
modes that have a mode frequency ratio very close to two ($\pm0.3$ppm). The
wavelength- and temperature-dependence of the refractive index means that the
frequency difference between these modes is an ultra-sensitive proxy of the
resonator temperature. This approach to temperature sensing automatically
suppresses sensitivity to thermal expansion and vibrationally induced changes
of the resonator. We also demonstrate active suppression of temperature
fluctuations in the resonator by controlling the intensity of the driving
laser. The residual temperature fluctuations are shown to be below the limits
set by fundamental thermodynamic fluctuations of the resonator material.
