  The properties of impurity immersed in the dilute $D$-dimensional Bose gas at
temperatures close to the second-order phase transition point are considered.
Particularly by means of the $1/N$-expansion we calculated the leading-order
polaron energy and the damping rate in the limit of vanishing boson-boson
interaction. It is show that the perturbative effective mass and the
quasiparticle residue diverge logarithmically in the long-length limit
signalling the non-analytic behavior of impurity spectrum and a non-pole
structure of a polaron Green's function in the infrared region, respectively.
