We consider the evolution of the detached ultra-short periodic white dwarf -- white dwarf binary system powered by unipolar unductor mechanism, as suggested by Wu et al. (2001). The two small hot spots on the surface of the more massive magnetic white dwarf, which rotates slightly asyncronously with the orbit, may be heated by currents which flow between and through both white dwarfs. The emission of gravitational waves leads to permanent increase of the angular orbital velocity and pushes magnetic white dwarf out of synchronysm with the orbital rotation. We show, that in this case the degree of asynchronysm between spin of the magnetic white dwarf and orbital rotation is not free parameter, but can be determined self-consistently. We found the analytical solution, which is exact if the magnetic moment of the magnetic white dwarf is not too small (\ge 10³⁰ G cm³). We also demonstrated that the magnetic field of the magnetic white dwarf must be not very strong (\mu\sim 10³⁰ G cm³) in order this effect produces appreciable heating.

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