  We introduce a hybrid plasmonic-photonic cavity setup that can be used to
induce and control long-distance heat transfer between molecular systems
through optomechanical interactions. The structure consists of two separated
plasmonic nanoantennas coupled to a dielectric cavity. The hybrid modes of this
resonator can combine the large optomechanical coupling of the sub-wavelength
plasmonic modes with the large quality factor and delocalized character of the
cavity mode that extends over a large distance ($\sim\mu$m). We show that this
can lead to effective long-range heat transport between molecular vibrations
that can be actively controlled through an external driving laser.
