  We observed two full orbital phase curves of the transiting brown dwarf
KELT-1b, at 3.6um and 4.5um, using the Spitzer Space Telescope. Combined with
previous eclipse data from Beatty et al. (2014), we strongly detect KELT-1b's
phase variation as a single sinusoid in both bands, with amplitudes of
$964\pm36$ ppm at 3.6um and $979\pm54$ ppm at 4.5um, and confirm the secondary
eclipse depths measured by Beatty et al. (2014). We also measure noticeable
Eastward hotspot offsets of $28.4\pm3.5$ degrees at 3.6um and $18.6\pm5.2$
degrees at 4.5um. Both the day-night temperature contrasts and the hotspot
offsets we measure are in line with the trends seen in hot Jupiters (e.g.,
Crossfield 2015), though we disagree with the recent suggestion of an offset
trend by Zhang et al. (2018). Using an ensemble analysis of Spitzer phase
curves, we argue that nightside clouds are playing a noticeable role in
modulating the thermal emission from these objects, based on: 1) the lack of a
clear trend in phase offsets with equilibrium temperature, 2) the sharp
day-night transitions required to have non-negative intensity maps, which also
resolves the inversion issues raised by Keating & Cowan (2017), 3) the fact
that all the nightsides of these objects appear to be at roughly the same
temperature of 1000K, while the dayside temperatures increase linearly with
equilibrium temperature, and 4) the trajectories of these objects on a Spitzer
color-magnitude diagram, which suggest colors only explainable via nightside
clouds.
