On the basis of Whole Earth Telescope observations of the g-mode oscil
lation spectrum of the white dwarf GD 358, Winget et al. find evidence
for significant differential rotation and for a time-varying magnetic
field concentrated in the surface layers of this star. Here we argue
on theoretical grounds that this magnetic field is produced by an alph
aomega dynamo operating in the lower part of a surface convection zone
in GD 358. Our argument is based on numerical solutions of the nonlin
ear, local dynamo equations of Robinson & Durney, with specific parame
ters based on our detailed models of white-dwarf convective envelopes,
and universal constants determined by a calibration with the Sun's dy
namo. The calculations suggest a dynamo cycle period of about 6 years
for the fundamental mode, and periods as short as 1 year for the highe
r-order modes that are expected to dominate in view of the large dynam
o number we estimate for GD 358. These dynamo periods are consistent w
ith the changes in the magnetic field of GD 358 over the span of 1 mon
th inferred by Winget et al. from their observations. Our calculations
also suggest a peak dynamo magnetic field strength at the base of the
surface convection zone of about 1800 G, which is consistent with the
field strength inferred from the observations.