Joule dissipation rates in the magnetic flux tubes at different heights of the solar atmosphere, from the photosphere to the corona, are studied. It is assumed that generation of the electric currents is cased by convective motions at the photospheric foot-points of the flux tubes. It is shown that the role of ion-atom collisions in the Joule dissipation and solar plasma heating is decisive. The Cowling resistivity exceeds the classical (Spitzer) resistivity not only in the weakly ionized layers of the atmosphere but also in the corona with relative density of the neutral atoms about $10^{-7}$ cm$^{-3}$ if the electric currents $I \geq 2 \times 10^8$ A. As an illustration of the altitude dependence of the Cowling resistivity for different magnitudes of the electric current, we applied the atmospheric model developed by Avrett and Loeser (2008). We have shown that the maximal dissipation occurs in the transition layer. The role of Cowling resistivity in Joule dissipation increases with the filamentation of magnetic flux tubes.