We present results from integral field spectroscopy with the Potsdam Multi-Aperture Spectrograph of the head of the Herbig-Haro object HH202 with a spatial sampling of 1x1 arcsec^2. 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, t^2. We have calculated the t^2 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 of O^{2+}, ADF(O^{2+}), finding its maximum value at the HH202-S position. We have explored the relations between the ADF(O^{2+}) and the electron density, the Balmer and [O III] temperatures, the ionization degree as well as the t^2 parameter. We do not find clear correlations between these properties and the results seem to support that the ADF and t^2 are independent phenomena. We have found a weak negative correlation between the O^{2+} abundance determined from recombination lines and the temperature, which is the expected behaviour in an ionized nebula, hence it seems that there is not evidence for the presence of super-metal rich droplets in H II regions.