Exomoons represent an outstanding challenge in modern astronomy , with the potential to provide rich insights into planet formation theory and habitability . In this work , we stack the phase-folded transits of 284 viable moon hosting Kepler planetary candidates , in order to search for satellites . These planets range from Earth-to-Jupiter sized and from { \sim } 0.1-to-1.0 AU in separation - so-called “ warm ” planets . Our data processing includes two-pass harmonic detrending , transit timing variations , model selection and careful data quality vetting to produce a grand light curve with a r.m.s . of 5.1 ppm . We find that the occurrence rate of Galilean-analog moon systems for planets orbiting between { \sim } 0.1 and 1.0 AU can be constrained to be \eta < 0.38 to 95 % confidence for the 284 KOIs considered , with a 68.3 % confidence interval of \eta = 0.16 _ { -0.10 } ^ { +0.13 } . A single-moon model of variable size and separation locates a slight preference for a population of short-period moons with radii { \sim } 0.5 R _ { \oplus } orbiting at 5-10 planetary radii . However , we stress that the low Bayes factor of just 2 in this region means it should be treated as no more than a hint at this time . Splitting our data into various physically-motivated subsets reveals no strong signal . The dearth of Galilean-analogs around warm planets places the first strong constraint on exomoon formation models to date . Finally , we report evidence for an exomoon candidate Kepler-1625b I , which we briefly describe ahead of scheduled observations of the target with the Hubble Space Telescope .