Recently, the temperature T and the luminosity L X of the hot gas halos of early-type galaxies have been derived, with unprecedented accuracy, from Chandra data for a sample of 30 galaxies, covering a wider range of galactic luminosity (and central velocity dispersion σ c ) than before. This work investigates the origin of the observed temperatures by examining the relationship between them and the galaxy structure, the gas heating due to Type Ia supernovae (SNe Ia) and the gravitational potential, and the dynamical status of the gas flow. In galaxies with σ c 200 km s −1 , the T's are close to a fiducial average temperature of gas in outflow; at 200 < σ c (km s −1 ) < 250, the T's are generally lower than this and unrelated to σ c , which requires a more complex gas flow status; at larger σ c , the T's may increase as σ 2 c , as expected for infall heating, though heating from SNe Ia, that is independent of σ c , should be dominant. All observed T's are larger than the virial temperature, by up to ∼0.5 keV. The additional heating can be provided in the X-ray brightest galaxies by SNe Ia and infall heating, with an SN Ia energy input even lower than in standard assumptions; in the X-ray fainter ones it can be provided by SNe Ia, whose energy input would be required to be close to the full standard value at the largest σ c . This same energy input, though, would produce temperatures larger than observed at low σ c if entirely thermalized. The values of the observed T's increase from outflows to inflows; the gas is relatively hotter in outflows, however, if the T's are rescaled by the virial temperature. For 200 < σ c (km s −1 ) < 250, lower L X values tend to correspond to lower T's, a result that deserves further investigation.