  (Abridged) We present an exploration of the internal rotation of GD 278, the
first pulsating extremely low-mass white dwarf that shows rotational splittings
within its periodogram. We assess the theoretical frequency splittings expected
for different rotation profiles and compare them to the observed frequency
splittings of GD 278. To this aim, we employ an asteroseismological model
representative of the pulsations of this star, obtained by using the LPCODE
stellar evolution code. We also derive a rotation profile that results from
detailed evolutionary calculations carried out with the MESA stellar evolution
code and use it to infer the expected theoretical frequency splittings. We
found that the best-fitting solution when assuming linear profiles for the
rotation of GD 278 leads to values of the angular velocity at the surface and
the center that are only slightly differential, and still compatible with rigid
rotation. The values of the angular velocity at the surface and the center for
the simple linear rotation profiles and for the rotation profile derived from
evolutionary calculations are in very good agreement. Also, the resulting
theoretical frequency splittings are compatible with the observed frequency
splittings, in general, for both cases. The results obtained from the different
approaches followed in this work to derive the internal rotation of GD 278
agree. The fact that they were obtained employing two independent stellar
evolution codes gives robustness to our results. Our results suggest only a
marginally differential behavior for the internal rotation in GD 278, and
considering the uncertainties involved, very compatible with the rigid case, as
has been observed previously for white dwarfs and pre-white dwarfs. The
rotation periods derived for this star are also in line with the values
determined asteroseismologically for white dwarfs and pre-white dwarfs in
general.
