  We have used the Spitzer Space Telescope in February 2016 to obtain high
cadence, high signal-to-noise, 17-hour duration light curves of Neptune at 3.6
and 4.5 $\mu$m. The light curve duration was chosen to correspond to the
rotation period of Neptune. Both light curves are slowly varying with time,
with full amplitudes of 1.1 mag at 3.6 $\mu$m and 0.6 mag at 4.5 $\mu$m. We
have also extracted sparsely sampled 18-hour light curves of Neptune at W1 (3.4
$\mu$m) and W2 (4.6 $\mu$m) from the WISE/NEOWISE archive at six epochs in
2010-2015. These light curves all show similar shapes and amplitudes compared
to the Spitzer light curves but with considerable variation from epoch to
epoch. These amplitudes are much larger than those observed with Kepler/K2 in
the visible (amplitude $\sim$0.02 mag) or at 845 nm with the Hubble Space
Telescope in 2015 and at 763 nm in 2016 (amplitude $\sim$ 0.2 mag). We
interpret the Spitzer and WISE light curves as arising entirely from reflected
solar photons, from higher levels in Neptune's atmosphere than for K2. Methane
gas is the dominant opacity source in Neptune's atmosphere, and methane
absorption bands are present in the HST 763, and 845 nm, WISE W1, and Spitzer
3.6 $\mu$m filters.
