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 temperature gradient. Under certain circumstances, the shear drives the heat up the radial temperature gradient into a cross section of the magnetic flux 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 term, and its strength is proportional to the cube of the temperature. We apply 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.