Luhman and collaborators recently discovered an early-T dwarf companion to the G0 dwarf star HN Peg , using Spitzer Infrared Array Camera ( IRAC ) images . Companionship was established on the basis of the common proper motion inferred from 1998 Two Micron All Sky Survey images and the 2004 IRAC images . In this paper we present new near-infrared imaging data which confirms the common proper motion of the system . We also present new 3 - 4 \mu m spectroscopy of HN Peg B , which provides tighter constraints on both the bolometric luminosity determination and the comparison to synthetic spectra . New adaptive optics imaging data are also presented , which shows the T dwarf to be unresolved , providing limits on the multiplicity of the object . We use the age , distance and luminosity of the solar-metallicity T dwarf to determine its effective temperature and gravity , and compare synthetic spectra with these values , and a range of grain properties and vertical mixing , to the observed 0.8 - 4.0 \mu m spectra and mid-infrared photometry . We find that models with temperature and gravity appropriate for the older end of the age range of the system ( 0.5 Gyr ) can do a reasonable job of fitting the data , but only if the photospheric condensate cloud deck is thin , and if there is significant vertical mixing in the atmosphere . Dwarfs such as HN Peg B , with well-determined metallicity , radius , gravity and temperature will allow development of dynamical atmosphere models , leading to the solution of the puzzle of the L to T dwarf transition .