  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. High-quality integral field spectroscopy (IFS) data with a
wide spectral and spatial coverage, such as those from the CALIFA survey, offer
an unprecedented opportunity for advancing our understanding of the wim in
ETGs. This article centers on a 2D investigation of the wim component in 32
nearby (<~150Mpc) ETGs from CALIFA, complementing a previous 1D analysis of the
same sample (Papaderos et al. 2013; P13). We include here H\alpha\ intensity
and equivalent width (EW) maps and radial profiles, diagnostic emission-line
ratios, besides ionized-gas and stellar kinematics. This study is supplemented
by \tau-ratio maps as an efficient means to quantify the role of
photoionization by pAGB stars, as compared to other mechanisms (e.g., AGN,
low-level star formation). Additionally, we extend the tentative classification
proposed in P13 by the type i+, which is assigned to a subset of type i ETGs
exhibiting ongoing low-level star-formation (SF) in their periphery. This
finding along with faint traces of localized SF in the extranuclear component
of several of our sample ETGs points to a non-negligible contribution by OB
stars to the total ionizing budget. We also demonstrate that, at the typical
emission-line detection threshold of ~2\AA in previous studies, most of the
extranuclear wim emission in an ETG may evade detection, which could in turn
prompt its classification as an entirely gas-devoid system. This study adds
further observational evidence for a considerable heterogeneity among ETGs with
regard to the physical properties and 2D kinematics of the wim component, and
underscores the importance of IFS studies over their entire optical extent.
