We present results from integral field spectroscopy with the Potsdam Multi-Aperture Spectrograph of the head of the Herbig-Haro (HH) object HH202 with a spatial sampling of 1 × 1arcsec2. We have obtained maps of different emission lines, physical conditions - such as electron temperature and density - and ionic abundances from recombination and collisionally excited lines. We present the first map of the Balmer temperature and of the temperature fluctuation parameter, t2. We have calculated the t2 in the plane of the sky, which is substantially smaller than that determined along the line of sight. We have mapped the abundance discrepancy factor (ADF) of O2+, ADF(O2+), finding its maximum value at the HH202-S position. We have explored the relations between the ADF(O2+) and the electron density, the Balmer and [OIII] temperatures, the ionization degree as well as the t2 parameter. We do not find clear correlations between these properties and the results seem to support that the ADF and t2 are independent phenomena. We have found a weak negative correlation between the O2+ abundance determined from recombination lines and the temperature, which is the expected behaviour in an ionized nebula, hence it seems that there is no evidence for the presence of supermetal-rich droplets in HII regions. Based on observations collected at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC). E-mail: amd [at] iac.es (amd[at]iac[dot]es)