Using data from contemporaneous observations with Chandra and Swift, it is shown that the X‐ray emission below 10 keV is predominantly thermal, characterized by flares and emission lines and dominated by the soft component. The Chandra and Swift X‐ray spectra (EX≤ 10 keV) can be reproduced by multicomponent thermal emission models with a time‐averaged X‐ray luminosity of LX∼ 1031 erg s−1. The pulsed 33‐s soft X‐ray emission below 10 keV is confirmed in both the Chandra and Swift data sets. The epoch of pulse maximum of the 33‐s white dwarf spin period is consistent with the recently derived ephemeris based upon Suzaku measurements. The recently detected Suzaku hard X‐ray component above 10 keV shows a non‐thermal power‐law nature, with a photon index of Γ∼ 1.2, possibly the result of synchrotron emission of high‐energy electrons in the white dwarf magnetosphere. The hard X‐ray luminosity of LX,hard≤ 5 × 1030 erg s−1 also constitutes κ∼ 0.1 per cent of the total spin‐down luminosity of the white dwarf. This places AE Aquarii in the same category as young spin‐powered pulsars between 2 and 20 keV. Additionally, it is shown that electrons can be accelerated to energies in excess of 10 TeV outside the light cylinder radius, providing interesting possibilities for VHE‐TeV follow‐up observations. The X‐ray emission below EX≤ 10 keV, on the other hand, is explained in terms of plasma heating at the magnetospheric radius, the result of the dissipation of gravitational potential energy. It is found that a conversion efficiency of α∼ 0.01 is sufficient to heat the plasma at the magnetospheric boundary to temperatures kT≤ 10 keV, sufficient to drive the X‐ray emission below 10 keV. Only a small fraction (β∼ 0.3 per cent) of the mass flow at the magnetospheric radius eventually accretes on to the surface of the white dwarf, emphasizing the very effective magnetospheric propeller process in the system.