We find a new heat source term for hot coronal loops and include it in the
energy equation. This term requires the loop to be hotter than the ambient
corona and depends on the combined effect of electron fluid shear and the t
emperature gradient. Under certain circumstances, the shear drives the heat
up the radial temperature gradient into a cross section of the magnetic fl
ux tube from which it leaves by radiation and by conduction down the axial
temperature gradient in the usual manner. The heat source is thus a surface
term applied over the whole of the loop rather than a volume-distributed t
erm, and its strength is proportional to the cube of the temperature. We ap
ply it to the usual scaling law and obtain an expression for the radius of
the flux tube for thermal equilibrium to hold. The temperature distribution
around the plasma loop is determined and compared with recent observations
and is found to be in satisfactory agreement with them.