Hot dust-obscured galaxies (Hot DOGs) are a population of hyper-luminous infrared galaxies identified by the Wide-field Infrared Survey Explorer (WISE) mission from their very red mid-IR colors, and characterized by hot dust temperatures (T > 60 K). Several studies have shown clear evidence that the IR emission in these objects is powered by a highly dust-obscured active galactic nucleus (AGN) that shows close to Compton-thick absorption at X-ray wavelengths. Thanks to the high AGN obscuration, the host galaxy is easily observable, and has UV/optical colors usually consistent with those of a normal galaxy. Here we discuss a sub-population of eight Hot DOGs that show enhanced rest-frame UV/optical emission. We discuss three scenarios that might explain the excess UV emission: (i) unobscured light leaked from the AGN by reflection over the dust or by partial coverage of the accretion disk; (ii) a second unobscured AGN in the system; or (iii) a luminous young starburst. X-ray observations can help discriminate between these scenarios. We study in detail the blue excess Hot DOG WISE J020446.13–050640.8, which was serendipitously observed by Chandra/ACIS-I for 174.5 ks. The X-ray spectrum is consistent with a single, hyper-luminous, highly absorbed AGN, and is strongly inconsistent with the presence of a secondary unobscured AGN. Based on this, we argue that the excess blue emission in this object is most likely either due to reflection or a co-eval starburst. We favor the reflection scenario as the unobscured star formation rate needed to power the UV/optical emission would be gsim1000 M⊙ yr−1. Deep polarimetry observations could confirm the reflection hypothesis. ; Peer-reviewed ; Publisher Version