  We present the microscopic treatment of edge magnetoplasmons (EMPs) for the
regime of not-too-low temperatures defined by the condition $\hbar
\omega_{c}\gg k_{B}T\gg \hbar v_{g}/2\ell_{0}$, where $v_{g}$ is the group
velocity of the edge states, $\ell_{0}=\sqrt{\hbar /m^{\ast}\omega_{c}}$ is the
magnetic length and $\omega_{c}$ is the cyclotron frequency. We find a weakly
damped symmetric mode, named helical edge magnetoplasmon, which is localized at
the edge states region for filling factors $\nu =1, 2$ and \textit{very strong
dissipation} $\eta_{T}=\xi /k_{x}\ell_{T}\agt\ln (1/k_{x}\ell_{T})\gg 1$, where
the characteristic length $\ell_{T}=k_{B}T\ell_{0}^{2}/\hbar v_{g}\gg
\ell_{0}/2$ with $\xi $ being the ratio of the local transverse conductivity to
the local Hall conductivity at the edge states and $k_{x}$ is the wave vector
along the edge; here other EMP modes are strongly damped. The spatial structure
of the helical edge magnetoplasmon, transverse to the edge, is strongly
modified as the wave propagates along the edge. In the regime of \textit{weak
dissipation}, $\eta_{T}\ll 1$, we obtain exactly the damping of the fundamental
mode as a function of $k_{x}$. For $\nu=4$ and weak dissipation we find that
the fundamental modes of $n=0$ and $n=1$ Landau levels (LLs) are strongly
renormalized due to the Coulomb coupling. Renormalization of all these EMPs
coming from a metal gate and air half-space is studied.
