  The influence of thermo-optic effects on shape profiles of soliton crystals
in optical Kerr microresonators is investigated. The study rests on a model
that consists of the Lugiato-Lefever equation, coupled to the one-dimensional
heat diffusion equation with a source term proportional to the average power of
the optical field. Using appropriate variable changes the model equations are
transformed into a set of coupled first-order nonlinear ordinary differential
equations. These equations are solved numerically with emphasis on the
influence of thermo-optic effects on the amplitude and instantaneous frequency
of the optical field, as well as on the temperature profile in the
microresonator cavity. It is found that thermo-optic effects do not prevent
soliton crytals from forming in optical Kerr microresonators, however, a strong
thermal detuning will decrease the soliton-crystal amplitude. The model
predicts a temperature profile in the microresonator cavity which is
insensitive to the specific spatio-temporal profile of the soliton crystal
propagating in the microresonator, a feature peculiar to the model.
