  We investigate the temperature dependence of the thermal dilepton rate and
the electrical conductivity of the gluon plasma at temperatures of $1.1T_c$,
$1.3T_c$ and $1.5T_c$ in quenched QCD. Making use of non-perturbatively
clover-improved Wilson valence quarks allows for a clean extrapolation of the
vector meson correlation function to the continuum limit. We found that the
vector correlation function divided by $T^3$ is almost temperature independent
in the current temperature window. The spectral functions are obtained by
$\chi^2$ fitting of phenomenologically inspired Ans\"atze for the spectral
function to the continuum extrapolated correlator data, where the correlations
between the data points have been included. Systematic uncertainties arising
from varying the Ans\"atze motivated from strong coupling theory as well as
perturbation theory are discussed and estimated. We found that the electrical
conductivity of the hot medium, related to the slope of the vector spectral
function at zero frequency and momentum, is $0.2C_{em}\lesssim
\sigma/T\lesssim0.7C_{em}$ for $T=1.1T_c$ and $0.2C_{em}\lesssim
\sigma/T\lesssim0.4C_{em}$ for the higher temperatures. The dilepton rates and
soft photon rates, resulting from the obtained spectral functions, show no
significant temperature dependence, either.
