  Spin qubits associated with color centers are promising platforms for various
quantum technologies. However, to be deployed in robust quantum devices, the
variations of their intrinsic properties with the external conditions, and in
particular temperature, should be known with high precision. Unfortunately, a
predictive theory on the temperature dependence of the resonance frequency of
electron and nuclear spin defects in solids remains lacking. In this work, we
develop a first-principles method for the temperature dependence of zero phonon
line, zero-field splitting, hyperfine interaction, and nuclear quadrupole
interaction of color centers. As a testbed, we compare our ab-initio
calculation results with experiments in the Nitrogen-Vacancy (NV) center
finding good agreement. Interestingly, we identify the major origin of
temperature dependence as a second-order effect of phonon vibration. The method
is generally applicable to different color centers and provides a theoretical
tool for designing high-precision quantum sensors.
