  Transport properties of the good thermoelectric misfit oxide
Ca$_3$Co$_4$O$_9$ are examined. In-plane resistivity and Hall resistance
measurements were made on epitaxial thin films which were grown on {\it c}-cut
sapphire substrates using the pulsed laser deposition technique. Interpretation
of the in-plane transport experiments relates the substrate-induced strain in
the resulting film to single crystals under very high pressure ($\sim$ 5.5 GPa)
consistent with a key role of strong electronic correlation. They are confirmed
by the measured high temperature maxima in both resistivity and Hall
resistance. While hole-like charge carriers are inferred from the Hall effect
measurements over the whole investigated temperature range, the Hall resistance
reveals a non monotonic behavior at low temperatures that could be interpreted
with an anomalous contribution. The resulting unconventional temperature
dependence of the Hall resistance seems thus to combine high temperature
strongly correlated features above 340 K and anomalous Hall effect at low
temperature, below 100 K.
