  We investigate the dissipative dynamics of a corotating vortex pair in a
highly oblate axisymmetric Bose-Einstein condensate trapped in a harmonic
potential. The initial vortex state is prepared by creating a doubly charged
vortex at the center of the condensate and letting it dissociate into two
singly charged vortices. The separation of the vortex pair gradually increases
over time and its increasing rate becomes higher with increasing the sample
temperature $T$. The evolution of the vortex state is well described with a
dissipative point vortex model including longitudinal friction on the vortex
motion. For condensates of sodium atoms having a chemical potential of
$\mu\approx k_B\times 120$ nK, we find that the dimensionless friction
coefficient $\alpha$ increases from 0.01 to 0.03 over the temperature range of
200 nK $<T<$ 450 nK.
