  We propose and analyze a new way of using $\pi$ stacking to design molecular
junctions that either enhance or suppress a phononic heat current, but at the
same time remain conductors for an electric current. Such functionality is
highly desirable in thermoelectric energy converters, as well as in other
electronic components where heat dissipation should be minimized or maximized.
We suggest a molecular design consisting of two masses coupled to each other
with one mass coupled to each lead. By having a small coupling (spring
constant) between the masses, it is possible to either reduce, or perhaps more
surprisingly enhance the phonon conductance. We investigate a simple model
system to identify optimal parameter regimes and then use first principle
calculations to extract model parameters for a number of specific molecular
realizations, confirming that our proposal can indeed be realized using
standard molecular building blocks.
