The anomalous Hall effect in metal-insulator-semiconductor structures having thin (Ga,Mn)As layers as a channel has been studied in a wide range of Mn and hole densities changed by the gate electric field. Strong and unanticipated temperature dependence, including a change of sign, of the anomalous Hall conductance sigma(xy) has been found in samples with the highest Curie temperatures. For more disordered channels, the scaling relation between sigma(xy) and sigma(xx), similar to the one observed previously for thicker samples, is recovered.