  In a previous work (MGV18), we showed numerically that the turbulent cascade
generated by quasi-2D structures (with wave vectors mostly-perpendicular to the
mean magnetic field) is able to generate a temperature profile close to the one
observed in solar wind ($\simeq 1/R$) in the range 0.2 $\le R \le$ 1 au.
Theory, observations and numerical simulations point to another robust
structure, the radial-slab, with dominant wave vectors along the radial: we
study here the efficiency of the radial-slab cascade in building the $1/R$
temperature profile. As in MGV18, we solve the three-dimensional MHD equations
including expansion to simulate the turbulent evolution. We find that an
isotropic distribution of wave vectors with large cross helicity at 0.2 au,
along with a large wind expansion rate, lead again to a temperature decay rate
close to $1/R$ but with a radial-slab anisotropy at 1 au. Surprisingly, the
turbulent cascade concentrates in the plane transverse to the radial direction,
displaying 1D spectra with scalings close to $k^{-5/3}$ in this plane. This
supports both the idea of turbulent heating of the solar wind, and the
existence of two different turbulent cascades, quasi-2D and radial slab, at the
origin of the heating.
  We conclude that sampling the radial spectrum in the solar wind may give but
a poor information on the real cascade regime and rate when the radial slab is
a non-negligible part of turbulence.
