  We present $Spitzer$ IRS 5--14 $\mu$m spectra and 16 $\mu$m and 22 $\mu$m
photometry of the T2.5 companion to the $\sim$300 Myr-old G0V star HN Peg. We
incorporate previous 0.8--5 $\mu$m observations to obtain the most
comprehensive spectral energy distribution of an intermediate-gravity
L/T-transition dwarf which, together with an accurate Gaia EDR3 parallax of the
primary, enable us to derive precise fundamental parameters. We find that young
($\approx$0.1--0.3 Gyr) early-T dwarfs on average have $\approx$140 K lower
effective temperatures, $\approx$20% larger radii, and similar bolometric
luminosities compared to $\gtrsim$1 Gyr-old field dwarfs with similar spectral
types. Our accurate infrared spectrophotometry offers new detail at wavelengths
where the dominant carbon-bearing molecules have their strongest transitions:
at 3.4 $\mu$m for methane and at 4.6 $\mu$m for carbon monoxide. We assess the
performance of various widely available photospheric models and find that
models with condensates and/or clouds better reproduce the full SED of this
moderately young early-T dwarf. However, cloud-free models incorporating a more
general convective instability treatment reproduce at least the low-resolution
near-IR spectrum similarly well. Our analysis of $R\approx2300$ $J$-band
spectra shows that the near-infrared potassium absorption lines in HN Peg B
have similar strengths to those seen in both younger and older T2-T3 dwarfs. We
conclude that while alkali lines are well-established as surface gravity
indicators for L-type or warmer stars, they are insensitive to surface gravity
in early-T dwarfs
