The hybrid microcavity composed of different materials shows unique thermal-optical properties such as resonance frequency shift and small thermal noise fluctuations with the temperature variation. Here, we have fabricated the hybrid Si3N4 - TiO2 microring, which decreases the effective thermo-optical coefficients (TOC) from 23.2pm/K to 11.05pm/K due to the opposite TOC of these two materials. In this hybrid microring, we experimentally study the thermal dynamic with different input powers and scanning speeds. The distorted transmission and thermal oscillation are observed, which results from the non-uniform scanning speed and the different thermal relaxation times of the Si3N4 and the TiO2. We calibrate the distorted transmission spectrum for the resonance measurement at the reverse scanning direction and explain the thermal oscillation with a thermal-optical coupled model. Finally, we analyse the thermal oscillation condition and give the diagram about the oscillation region, which has significant guidance for the occurrence and avoidance of the thermal oscillation in practical applications.