X-ray emitting atmospheres of non-rotating early-type galaxies and their connection to central active galactic nuclei have been thoroughly studied over the years. However, in systems with significant angular momentum, processes of heating and cooling are likely to proceed differently. We present an analysis of the hot atmospheres of six lenticulars and a spiral galaxy to study the effects of angular momentum on the hot gas properties. We find an alignment between the hot gas and the stellar distribution, with the ellipticity of the X-ray emission generally lower than that of the optical stellar emission, consistent with theoretical predictions for rotationally supported hot atmospheres. The entropy profiles of NGC 4382 and the massive spiral galaxy NGC 1961 are significantly shallower than the entropy distribution in other galaxies, suggesting the presence of strong heating (via outflows or compressional) in the central regions of these systems. Finally, we investigate the thermal (in)stability of the hot atmospheres via criteria such as the TI- and C-ratio, and discuss the possibility that the discs of cold gas present in these objects have condensed out of the hot atmospheres.