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We experimentally demonstrate a push-pull optical nonreciprocal transmission (ONT) mechanism induced by thermo-optic effect in cascaded silicon microring resonators (MRRs). A nonreciprocal extinction ratio of up to 27 dB and an operation bandwidth larger than 0.15 nm are achieved in the proposed ONT system. The device can operate with a resonance mismatch between the two cascaded MRRs from 0.14 nm to 0.55 nm. The proposed ONT device could potentially find applications in optical diodes and bidirectional control of light in future on-chip all-optical information processing systems.