  A theoretical model that describes the evolution of a suspension in which
crystals can sediment to form a dense cumulate or may produce a light flotation
crust has been derived in a companion paper. We use this model to study the
thermal history of early accreted planetary bodies accreted during the very
early stages of the formation of the solar system. We study the conditions
required to form and preserve flotation crusts and basal cumulates, and the
implications for the thermal evolution of planetesimals. We calculate the
temperature evolution in an early accreted planetesimals internally heated by
the decay of $\rm{^{26}Al}$ and $\rm{^{60}Fe}$. For planetesimal with radius
$R>30\, \rm{km}$, partial melting reaches 40%, planetesimals undergo a
rheological transition and form a magma ocean, i.e.: a suspension from which
crystals can segregate and form a floating crust and/or a dense cumulate.
Because of the formation of an insulation floating crust, this magma ocean
episode is characterized by a relatively long time life, a slow cooling rate,
and a weak surface heat flux. The model further predicts a cyclic evolution
where episodes of crustal thickening alternate with episodes of melting-induced
crustal thinning. These cycles produce in turn an oscillating thermal history
and prevent runaway thermal heating of the planetesimals. At the end of the
magma ocean episode, when the fraction of crystals becomes larger than 60\%, a
transition occurs to solid-state convection in the planetesimal's mantle. This
stage is characterized by high viscous shear stress that tends to erode
previously formed crystal deposits. However, the time scale of this erosion
process is larger that the lifetime of the planetesimal. Hence solid-state
evolution can be described by a well mixed mantle embedded by a metastable
crust and a preserved cumulate at its base.
