  We perform a systematic search for atmospheric variability in short-period
gas-giant planets (hot Jupiters) observed by the Kepler mission, by looking for
temporal variability of their secondary eclipse depths. This is motivated by a
recent detection of a decrease in the dayside brightness of KELT-1 b between
TESS Sectors 17 and 57, separated by about 3 years. We fit the Kepler light
curves of 53 hot Jupiters and measure their secondary eclipse depths during
individual Kepler quarters and 4-quarter windows. We detect the secondary
eclipses in individual quarters or four-quarter windows for 17 out of the 53
systems. In those 17 systems we do not detect statistically significant
astrophysical variation in the secondary eclipse depths. We show that the data
is sensitive to the variability seen for KELT-1 b in TESS data. Therefore, the
absence of detected secondary eclipse variability in Kepler data suggests that
the atmospheric variability in KELT-1 b is not common. In addition, several of
the 53 targets we investigated display variability in their transit depths with
a period of 4 quarters (1 year). This instrumental signal is likely present in
the light curves of other transiting planets we did not analyze and other
variable stars observed by Kepler. Finally, we find that Kepler-488 b has a
secondary eclipse depth that is unphysically large for a planet, and thus is
likely a misclassified red dwarf.
