We report infrared spectroscopic properties of the strongly correlated layered cobalt oxide [BiBa$_{0.66}$K$_{0.36}$O$_2$]CoO$_2$. These measurements performed on single crystals allow us to determine the optical conductivity as a function of tempera
ture. In addition to a large temperature dependent transfer of spectral weight, an unconventional low energy mode is found. We show that both its frequency and damping scale as the temperature itself. In fact, a basic analysis demonstrates that this mode fully scales onto a function of $omega$/T up to room temperature. This behavior suggests low energy excitations of non-Fermi liquid type originating from quantum criticality.
