The possibility that coronal heating occurs by means of anomalous Joule heating by electrostatic ion cyclotron waves is examined, with consideration given to currents running from foot of a loop to the other. It is assumed that self-fields generated by the currents are absent and currents follow the direction of the magnetic field, allowing the plasma cylinder to expand radially. Ion and electron heating rates are defined within the cylinder, together with longitudinal conduction and convection, radiation and cross-field transport, all in terms of Coulomb and turbulent effects. The dominant force is identified as electrostatic ion cyclotron instability, while ion acoustic modes remain stable. Rapid heating from an initial temperature of 10 eV to 100-1000 eV levels is calculated, with plasma reaching and maintaining a temperature in the 100 eV range. Strong heating is also possible according to the turbulent Ohm's law and by resistive heating.