For the field or Eulerian description of heat conduction, a method is discussed associated with description of thermal fields by a variational principle involving suitably constructed potentials rather than original physical variables. The considered processes are: simple hyperbolic heat transfer and coupled parabolic transfer of heat, mass and electric charge. By using various gradient or nongradient representations of original physical fields in terms of potentials, which are quantities of similar sort as those which Clebsch used in his representation of hydrodynamic velocity, suitable action-type criteria can be found, and corresponding Lagrangian and Hamiltonian formalisms can be developed. Symmetry principles can also be considered and components of energy-momentum tensor can be evaluated for a gauged lagrangian. The limiting reversible case appears as a suitable reference frame. The results suggest that thermodynamic irreversibility does not change neither kinetic potential nor action functional; it only complicates potential representations of physical fields in comparison with those describing the reversible evolution.