  We present algorithms for the ab-initio determination of the temperature
($T$) dependence of the mutual-friction coefficients $\alpha$ and $\alpha'$ and
the normal-fluid density $\rho_{\rm n}$ in the two-dimensional (2D)
Galerkin-truncated Gross-Pitaevskii system. Our algorithms enable us to
determine $\alpha(T)$, even though fluctuations in 2D are considerably larger
than they are in 3D. We also examine the implications of our measurements of
$\alpha'(T)$ for the Iordanskii force, whose existence is often questioned.
