  The aim of this work is to introduce a thermo-electromagnetic model for
calculating the temperature and the power dissipated in cylindrical pieces
whose geometry var\'ies with time and undergoes large deformations; the motion
will be a known data. The work will be a first step towards building a complete
thermoelectromagnetic-mechanical model suitable for simulating electrically
assisted forming processes, which is the main motivation of the work. The
electromagnetic model will be obtained from the time-harmonic eddy current
problem with an inplane current; the source will be given in terms of currents
or voltages defined at sorne parts of the boundary. Finite element methods
based on a Lagrangian weak formulation will be used for the numerical solution.
This approach will avoid the need to compute and remesh the
thermo-electromagnetic domain along the time. The numerical tools will be
implemented in FEniCS and validated by using a suitable test also solved in
Eulerian coordinates.
