The integration of ferroelectric polymer gates on a Mn-doped GaAs magnetic channel provides a promising route for the persistent field-effect control of magnetic properties in high-quality diluted magnetic semiconductors (DMSs) that are otherwise incompatible with traditional oxide ferroelectrics. That control demands the thinnest possible DMS layers, for which to date the Curie temperature (T-C) is severely depressed. Here we show that reducing the channel thickness from 7 to 3-4 nm by etching, followed by a brief 135 degrees C anneal, does not degrade the T-C (similar to 70 K) of the 7-nm film. The channel thinning results in a dramatic threefold increase of the T-C shift controlled by the ferroelectric polarization reversal. Furthermore, we obtain the same exponent (partial derivative 1n T-C/partial derivative 1n R) = gamma approximate to -0.3 for all channels with different thicknesses, regardless of the technique used for T-C determination. These results suggest that the ferromagnetic coupling in an ultrathin 3-nm channel is far from the two-dimensional limit and shows a rather bulklike behavior, similar to well-established 7-nm films.