  We explore the continuum limit $a\rightarrow 0$ of meson correlation
functions at finite temperature. In detail we analyze finite volume and lattice
cut-off effects in view of possible consequences for continuum physics. We
perform calculations on quenched gauge configurations using the clover improved
Wilson fermion action. We present and discuss simulations on isotropic
$N_\sigma^3\times 16$ lattices with $N_\sigma=32,48,64,128$ and $128^3 \times
N_\tau$ lattices with $N_\tau=16,24,32,48$ corresponding to lattice spacings in
the range of $0.01 fm \lsim a \lsim\ 0.031 fm$ at $T\simeq1.45T_c$. Continuum
limit extrapolations of vector meson and pseudo scalar correlators are
performed and their large distance expansion in terms of thermal moments is
introduced. We discuss consequences of this analysis for the calculation of the
electrical conductivity of the QGP at this temperature.
