  Understanding and controlling heat transport in molecular junctions would
provide new routes to design nanoscale coupled electronic and phononic devices.
Using first principles full quantum calculations, we tune thermal conductance
of a molecular junction by mechanically compressing and extending a short
alkane chain connected to graphene leads. We find that the thermal conductance
of the compressed junction drops by half in comparison to the extended
junction, making it possible to turn on and off the heat current. The low
conductance of the off state does not vary by further approaching the leads and
stems from the suppression of the transmission of the in--plane transverse and
longitudinal channels. Furthermore, we show that misalignment of the leads does
not reduce the conductance ratio. These results also contribute to the general
understanding of thermal transport in molecular junctions.
