Nonlinear effects limit the maximum amount of optical power that can be handled by silicon photonic integrated circuits (PICs). This limitation is particularly tight in resonant devices such as microring resonator (MRR) filters, suffering from a power-dependent resonance spread due to intracavity power enhancement. In this Letter, we present an automatic control system that can dynamically mitigate the nonlinear spectral distortion of silicon MRR filters by thermally controlling each MRR. The benefit of the proposed scheme is demonstrated on the spectral response of a polarization-transparent coupled-MRR filter operating on a 200 Gbit/s signal. The proposed technique, which does not require a priori information on the PIC topology and functionality, is scalable to more complex architectures and can be employed to compensate for generic nonlinear effects in different photonic platforms.