Self-injection locking is an effective tool of laser stabilization, known from the origins of radiophysics. Recently it was shown to be useful for perspective compact sources of optical frequency combs. This, however, implies the nonlinearity and high power inside the microresonator. Recently, we showed, that the account for the nonlinearity in the self-injection locking model substantially changes the system behaviour. However, thermal effects, inevitably arising from the high intracavity power, have not been considered yet. This point is also of great importance as these effects are known to be a serious obstacle for stable dissipative Kerr soliton generation. In this work we develop further the self-injection locking theory and show that thermal nonlinearity also introduce novel and important features. We analyse in detail several possible regimes arising due to thermal and Kerr nonlinearity competition and analyse tuning curves at different signs of thermorefractive coefficient. We confirm our predictions that the locking should help to overcome the temperature drift problem and show that nonlinear frequency shift helps to reach the desired detuning for the soliton comb state inside the locking band.
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