  The properties of the thermal Abelian color-magnetic monopoles in the
maximally Abelian gauge are studied in the deconfinement phase of the lattice
SU(2) gluodynamics. To check universality of the monopole properties we employ
the tadpole improved Symanzik action. The simulated annealing algorithm
combined with multiple gauge copies is applied for fixing the maximally Abelian
gauge to avoid effects of Gribov copies. We compute the density, interaction
parameters, thermal mass and chemical potential of the thermal Abelian
monopoles in the temperature range between Tc and 3Tc. In comparison with
earlier findings our results for these quantities are improved either with
respect to effects of Gribov copies or with respect to lattice artifacts.
