ABSTRACT We present full-sky maps of the Integrated Sachs–Wolfe effect (ISW) for the MICE Grand Challenge lightcone simulation up to redshift 1.4. The maps are constructed in the linear regime using spherical Bessel transforms. We compare and contrast this procedure against analytical approximations found in the literature. By computing the ISW in the linear regime, we remove the substantial computing and storage resources required to calculate the non-linear Rees–Sciama effect. Since the linear ISW at low redshift z ≲ 1, at large angular scales, and after matter domination is ${\sim}10^{2}\, \mathrm{ times}$ larger in ΔT/T, this has a negligible impact on the maps produced and only becomes relevant on scales which are dominated by cosmic microwave background (CMB) anisotropies. The MICE simulation products have been extensively used for studies involving current and future galaxy surveys. The availability of these maps will allow MICE to be used for future galaxy and CMB cross-correlation studies, ISW reconstruction studies, and ISW void-stacking studies probed by galaxy surveys such as Dark Energy Survey, Dark Energy Spectroscopic Instrument, Euclid, and Rubin Legacy Survey of Space and Time. The pipeline developed in this study is provided as a public Python package pyGenISW. This could be used in the future studies for constructing the ISW from existing and future simulation suites probing vast sets of cosmological parameters and models.