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It has been suggested that the isotropic electron halo observed in the solar wind electron velocity distribution function may originate from nanoflare-accelerated electron beams below 1.1 R from the solar surface through the nonlinear electron two-stream instability (ETSI). This model unifies the origins of kinetic waves, the electron halo, and the coronal weak Type III bursts, and establishes a link between the solar wind observables and the electron dynamics in nanoflares. One of the important predictions of this model is that the halo-core temperature ratio is anticorrelated with the density ratio, and the minimum ratio is ∼4, a relic of the ETSI heating and has been found to be consistent with solar wind observations. However, how the density and relative drift of the electron beams determine the thermal properties of solar wind electrons is unclear. In this paper, using a set of particle-in-cell simulations and kinetic theory, we show that a necessary condition for an isotropic halo to develop is that the ratio of beam density nb and the background n0 be lower than a critical value Nc ∼ 0.3. Heating of the core electrons becomes weaker with decreasing beam density, while the heating of halo electrons becomes stronger. As a result, the temperature ratio of the halo and core electrons increases with the decrease of the beam density, explaining the physical meaning of the predicted anticorrelated relation. We apply these results to the current observations and discuss the possible electron beam density produced in the nanoflares.