Finite Temperature and Density Effects in Planar Q.E.D

The behavior of finite temperature planar electrodynamics is investigated. We calculate the static as well as dynamic characteristic functions using real time formalism. The temperature and density dependence of dielectric and permeability functions, plasmon frequencies and their relation to the screening length is determined. The radiative correction to the fermion mass is also calculated. We also calculate the temperature dependence of the electron (anyon) magnetic moment. Our results for the gyromagnetic ratio go smoothly to the known result at zero temperature, $g=2$, in accordance with the general expectation.