  Thanks to their highly coherent emission and compact form factor, single
axial mode diamond Raman lasers have been identified as a valuable asset for
applications including integrated quantum technology, high resolution
spectroscopy or coherent optical communications. While the fundamental emission
linewidth of these lasers can be Fourier limited, their thermo-optic
characteristics lead to drifts in their carrier frequency, posing important
challenges for applications requiring ultra-stable emission. We propose here a
method for measuring accurately the temperature-dependent index of refraction
of diamond by employing standing Stokes waves produced in a monolithic
Fabry-Perot (FP) diamond Raman resonator. Our approach takes into account the
influence of the temperature on the first-order phonon line and the average
lattice phonon frequency under intense stimulated Raman scattering (SRS)
conditions. We further utilize this model to calculate the
temperature-dependent thermo-optic coefficient and the Gruneisen parameter of
diamond in the visible spectral range. The theory is accompanied by the
demonstration of tunable Fourier-limited Stokes nanosecond pulses with a
stabilized center frequency deviation of less than <4 MHz.
