  Modeling of gamma-ray burst (GRB) prompt emission spectra sometimes requires
a (quasi-) thermal spectral component in addition to the Band function. In
photospheric emission models, a prominent thermal component broadened by
sub-photospheric dissipation is expected to be released at the photospheric
radius, $r_{\rm ph}\sim10^{12}\,$cm. We consider an ultra-relativistic strongly
magnetized outflow with a striped-wind magnetic-field structure undergoing
gradual and continuous magnetic energy dissipation at $r<r_s$ that heats and
accelerates the flow, leading to a bulk Lorentz factor
$\Gamma(r)=\Gamma_\infty\min[1,(r/r_s)^{1/3}]$, where typically $r_{\rm
ph}<r_s$. Similar dynamics and energy dissipation rates are also expected in
highly-variable magnetized outflows without stripes/field-reversals. Two modes
of particle energy injection are considered: (a) power-law electrons, e.g.
accelerated by magnetic reconnection, and (b) continuous distributed heating of
all electrons (and $e^\pm$-pairs), e.g. due to MHD instabilities. Time-resolved
energy spectra are obtained using a numerical code that evolves coupled kinetic
equations for a photon-electron-positron plasma. We find that (i) the thermal
component peaks at $(1+z)E_{\rm pk}\sim0.2-1\,$MeV, for a source at redshift
$z$, and becomes subdominant if the total injected energy density exceeds the
thermal one, (ii) power-law electrons cool mainly by synchrotron emission
whereas mildly relativistic and almost monoenergetic electrons in the
distributed heating scenario cool by Comptonization on thermal peak photons,
(iii) both scenarios can yield a low-energy break at $E_{\rm br}\approx E_{\rm
th}$, and (iv) the $0.5(1+z)^{-1}\,$keV X-ray emission is suppressed in the
power-law injection case, but it is expected for the distributed heating
scenario. Energy-dependent linear polarization can differentiate between the
two energy injection cases.
