  The magnitude and the temperature dependence of the superconducting order
parameter {\Delta}(T) of single-crystals of Cd2Re2O7 (Tc = 1.02 K) was measured
using point contact spectroscopy. In order to fit the conductance spectra and
to extract the order parameter at different temperatures we generalized the
Blonder-Tinkham-Klapwijk theory by including the self-energy of the
quasiparticles into the Bogoliubov equations. This modification enabled
excellent fits of the conductance spectra. {\Delta}(T) increases steeply below
the superconducting transition temperature of 1.02 K and levels off below about
0.8 K depending on measurement directions where its value varied from 0.22(1)
meV to 0.26(1) meV. Our results indicate the presence of a strong
electron-phonon interaction and an enhanced quasiparticle damping and may be
related to a possible phase transition within the superconducting region at
about 0.8 K.
