  We calculate overstable convective modes of uniformly rotating hot Jupiters,
which have a convective core and a thin radiative envelope. Convective modes in
rotating planets have complex frequency $\omega$ and are stabilized by rapid
rotation so that their growth rates $\propto\omega_{\rm I}={\rm Im}(\omega)$
are much smaller than those for the non-rotating planets. The stabilized
convective modes excite low frequency gravity waves in the radiative envelope
by frequency resonance between them. We find that the convective modes that
excite envelope gravity waves remain unstable even in the presence of
non-adiabatic dissipations in the envelope. We calculate the heating rates due
to non-adiabatic dissipations of the oscillation energy of the unstable
convective modes and find that the magnitudes of the heating rates cannot be
large enough to inflate hot Jupiters sufficiently so long as the oscillation
amplitudes remain in the linear regime.
