We present MUSE deep integral-field unit spectroscopy of three planetary nebulae (PNe) with high-abundance discrepancy factors (ADF > 20): NGC 6778, M 1-42, and Hf 2-2. We have constructed flux maps for more than 40 emission lines, and use them to build extinction, electron temperature (Te), electron density (ne), and ionic abundances maps of a number of ionic species. The effects of the contribution of recombination to the auroral [N II] and [O II] lines on Te and the abundance maps of low-ionization species are evaluated using recombination diagnostics. As a result, low Te values and a downward gradient of Te are found toward the inner zones of each PN. Spatially, this nearly coincides with the increase of abundances of heavy elements measured using recombination lines in the inner regions of PNe, and strongly supports the presence of two distinct gas phases: a cold and metal-rich and a warm one with 'normal' metal content. We have simultaneously constructed, for the first time, the ADF maps of O+ and O2+ and found that they centrally peak for all three PNe under study. We show that the main issue when trying to compute realistic abundances from either ORLs or CELs is to estimate the relative contribution of each gas component to the H I emission, and we present a method to evaluate it. It is also found that, for the studied high-ADF PNe, the amount of oxygen in the cold and warm regions is of the same order.