  The fine structure of solar prominences is made by thin threads that outline
the magnetic field lines. Observations show that transverse waves of Alfv\'enic
nature are ubiquitous in prominence threads. These waves are driven at the
photosphere and propagate to prominences suspended in the corona. Heating due
to Alfv\'en wave dissipation could be a relevant mechanism in the cool and
partially ionized prominence plasma. We explore the construction of 1D
equilibrium models of prominence thin threads that satisfy energy balance
between radiative losses, thermal conduction, and Alfv\'en wave heating. We
assume the presence of a broadband driver at the photosphere that launches
Alfv\'en waves towards the prominence. An iterative method is implemented, in
which the energy balance equation and the Alfv\'en wave equation are
consecutively solved. From the energy balance equation and considering no wave
heating initially, we compute the equilibrium profiles along the thread of the
temperature, density, ionisation fraction. We use the Alfv\'en wave equation to
compute the wave heating rate, which is then put back in the energy balance
equation to obtain new equilibrium profiles. The process is repeated until
convergence to a self-consistent thread model heated by Alfv\'en waves is
achieved. We have obtained equilibrium models composed of a cold and dense
thread, a extremely thin PCTR, and an extended coronal region. The length of
the cold thread decreases with the temperature at the prominence core and
increases with the Alfv\'en wave energy flux. Equilibrium models are not
possible for sufficiently large wave energy fluxes when the wave heating rate
inside the cold thread becomes larger than radiative losses. The maximum value
of the wave energy flux that allows an equilibrium depends on the prominence
core temperature. This constrains the existence of equilibria in realistic
conditions.
