We present a study of the kinematics and the physical properties of the central region of the Hickson Compact Group 31 (HCG 31), focusing on the HCG 31A+ C system, using integral field spectroscopy data taken with the Gemini South Telescope. The main players in the merging event (galaxies A and C) are two dwarf galaxies, which have had one close encounter, given the observed tidal tails, and may now be in their second approach, and are possibly about to merge. We present new velocity fields and H alpha emission, stellar continuum, velocity dispersion, electron density, H alpha equivalent-width and age maps. Considering the high spatial resolution of the integral field unit data, we were able to measure various components and estimate their physical parameters, spatially resolving the different structures in this region. Our main findings are the following: (1) We report for the first time the presence of a super stellar cluster next to the burst associated with the HCG 31C central blob, related to the high values of velocity dispersion observed in this region as well as to the highest value of stellar continuum emission. This may suggest that this system is cleaning its environment through strong stellar winds that may then trigger a strong star formation event in its neighbourhood. (2) Among other physical parameters, we estimate L(H alpha) similar to 14 x 10(41) erg s(-1) and the star formation rate, SFR similar to 11 M-circle dot yr(-1) for the central merging region of HCG 31A+ C. These values indicate a high star formation density, suggesting that the system is part of a merging object, supporting previous scenarios proposed for this system.