  There are a variety of cosmological models for dark matter and dark energy in
which a possible interaction is considered between these two significant
components of the universe. We focus on five suggested models of interacting
dark matter and dark energy and derive the modified virial theorem for them by
developing a previous approach. It provides an opportunity to study the
evolution of this modified virial theorem with time and interacting constants
for different interacting models. Then we use this obtained virial condition to
investigate the modified mass-temperature relation in galaxy clusters via three
various methods. It reveals that the effect of interaction between dark matter
and dark energy merely appears in the normalization factor of $M\propto
T^{\frac{3}{2}}$. This relation also leads to a new constraint on the constants
of interacting models, which only depends on the concentration parameter and
density profile of the cluster. Then we use five observational data sets to
check some proposed figures for the constants of interaction which have been
resulted from other observational constraints. Finally, by fitting the
observational results to the modified mass-temperature relation, we obtain
values for interacting constants of three models and four specific cases of the
two remained models. In agreement with many other observational outcomes, we
find that according to observational data for masses and temperatures of the
galaxy clusters, energy transfer occurs from dark matter to dark energy in the
seven investigated models.
