  The Bose polaron has attracted theoretical and experimental interest because
the mobile impurity is surrounded by a bath that undergoes a
superfluid-to-normal phase transition. Although many theoretical works have
studied this system in its ground state, only few analyze its behavior at
finite temperature. We have studied the effect of temperature on a Bose polaron
system performing ab-initio Path Integral Monte Carlo simulations. This method
is able to approach the critical temperature without losing accuracy, in
contrast with perturbative approximations. We have calculated the polaron
energy for the repulsive and attractive branches and we have observed an
asymmetric behavior between the two branches. When the potential is repulsive,
the polaron energy decreases when the temperature increases, and contrariwise
for the attractive branch. Our results for the effective mass and the dynamical
structure factor of the polaron show unambiguously that its quasiparticle
nature disappears close to the critical temperature, in agreement with recent
experimental findings. Finally, we have also estimated the fraction of bosons
in the condensate as well as the superfluid fraction, and we have concluded
that the impurity hinders the condensation of the rest of bosons.
