  We apply our calculation of direct $J/\psi$ production in the improved color
evaporation mode at ${\mathcal O}(\alpha_s^3)$ in collinear factorization to
Pb+Pb collisions. The cold nuclear matter effects of nuclear modifications of
the parton densities and intrinsic transverse momentum broadening are included.
We find that the polarization is independent of these effects. Our calculations
are compared to the Pb+Pb polarization parameters extracted by the ALICE
Collaboration at $\sqrt{s_{NN}} = 5.02$ TeV.
