  Fractional calculus has been proved to be very effective in representing the
visco-elastic relaxation response of materials with memory such as polymers.
Moreover, in modelling the temperature dependency of the material functions in
thermo-visco-elasticity, the standard time-temperature superposition principle
is known to be ineffective in most of the cases (thermo-rehological
complexity). In this work, a novel finite element formulation and numerical
implementation is proposed for the simulation of transient thermal analysis in
thermo-rehologically complex materials. The parameters of the visco-elastic
fractional constitutive law are assumed to be temperature dependent functions
and an internal history variable is introduced to track the changes in
temperature which are responsible for the phase transition of the material. The
numerical approximation of the fractional derivative is employed via the so
called Gr\"unwald-Letnikov approximation. The proposed model is used to
numerically solve some test cases related to relaxation and creep tests
conducted on a real polymer (Etylene Vynil Acetate), which is used as the major
encapsulant of solar cells in photovoltaics.
