Simulations of the XY model have been carried out to study vortex-pair fluctuations above and below the critical Kosterlitz-Thouless transition temperature T_KT.  The net winding number of vortices at a given temperature in a given area is computed as a function of the area, squared and averaged over 1000 Monte Carlo instances.  At all temperatures the net squared winding number is found to scale as the perimeter of the area, in contradiction to a number of literature predictions that it should scale with the area above T_KT, but in agreement with a calculation by Dhar [1] that it should remain a perimeter law to infinite temperature.  We find that the slope of the perimeter variation displays a peak  near T / T_KT = 1.15, very close to the peak in the specific heat.

1. D. Dhar, Phys. Lett. A 81, 19 (1981).