The rho-meson self energy at finite temperature T and the charged-pion
chemical potential mu(Q) are evaluated. The analysis is based on the
conventional pi-rho effective Lagrangian and the functional-integral r
epresentation of the partition function in the one-pion-loop approxima
tion (that is, to the second order in the coupling constant g(rho pi p
i)). The rho-meson mass and the width are found to increase with incre
asing temperature and chemical potential mu Q. At large mu Q, these ch
anges may be two times as great as the purely temperature shift of Gal
e and Kapusta at vanishing mu Q.