Context. The morphological, spectroscopic, and kinematical properties of the warm interstellar medium (wim) in early-type galaxies (ETGs) hold key observational constraints to nuclear activity and the buildup history of these massive, quiescent systems. This article centers on a 2D investigation of the wim component in 32 nearby (?150 Mpc) ETGs from CALIFA, complementing a previous 1D analysis of the same sample. The analysis presented here includes Ha intensity and equivalent width (EW) maps and radial profiles, diagnostic emission-line ratios, and ionized-gas and stellar kinematics. It is supplemented by t-ratio maps, which are a more efficient means to quantify the role of photoionization by the post-AGB stellar component than alternative mechanisms (e.g., AGN, low-level star formation). This study adds further observational evidence for a considerable heterogeneity among ETGs with regard to the physical properties and 2D kinematics of their extended wim component, and it clearly shows that a comprehensive understanding of these systems requires IFS studies over their entire optical extent.