  We study under what conditions the thermal peeling is present for dissipative
local and quasi-local anisotropic spherical matter configurations. The thermal
peeling occurs when different signs in the velocity of fluid elements appears,
giving rise to the splitting of the matter configuration. The evolution is
considered in the quasi-static approximation and the matter contents are
radiant, anisotropic (unequal stresses) spherical local and quasi-local fluids.
The heat flux and the associated temperature profiles are described by causal
thermodynamics consistent with this approximation. It is found some particular,
local and quasi-local equation of state for ultra-dense matter configurations
exhibit thermal peeling when most of the radiated energy is concentrated at the
middle of the distribution. This effect, which appears to be associated with
extreme astrophysical scenarios (highly relativistic and very luminous
gravitational system expelling its outer mass shells), is very sensible to
energy flux profile and to the shape of the luminosity emitted by the compact
object.
