is yet to be achieved [@8]-[@16]. Some authors (see ref. [@9]) have concluded that the superconductivity is lost at $T\neq 0$, based upon the appearance of a temperature-dependent correction to the induced Chern-Simons coefficient that is not cancelled out by the bare term. In ref. [@11] it is argued, however, that this finite temperature correction is numerically negligible at $T<200$ $K$, and that the main reason for the lack of a Meissner effect is the development of a pole $\sim \left( \frac{1}{{\bf k}%
^{2}}\right) $ in the polarization operator component $\Pi _{00}$ at $T\neq
0 $. There, it is discussed how the existence of this pole leads to a so called partial Meissner effect with a constant magnetic field penetration throughout the sample that appreciably increases with temperature. On the other hand, in ref. [@8], it has been independently claimed that the anyon model cannot superconduct at finite temperature due to the existence of a long-range mode, found inside the infinite bulk at $T\neq 0$. The long range mode found in ref. [@8] is also a consequence of the existence of a pole $\sim \left( \frac{1}{{\bf k}^{2}}\right) $ in the polarization operator component $\Pi _{00}$ at $T\neq 0$.

The apparent 