We experimentally observe that Si micro-ring modulator (MRM) modulation characteristics are strongly influenced by the modulation data rate and the data pattern and determine this influence is due to the temperature increase caused by dynamic power dissipation within the Si MRM device. We also quantitatively determine the amount of Si MRM resonance wavelength shift due to different modulation data rates, data patterns, and modulation voltages. Our results should be of great help for achieving reliable and optimal modulation characteristics for Si MRMs.