Our work on the thermal conductivity of diamond nanowires was recently published in Physical Review B. You can access the article here, "Thermal conductivity of diamond nanowires from first principles". This work was done in collaboration with Natalio Mingo's group at CEA-Grenoble, David Broido (Boston College) and Lucas Lindsay (Naval Research Laboratory). One interesting aspect of this work is that the thermal conductivity in these nanowires depends strongly on the crystallographic orientation of the nanowire, even at room temperature. In particular, the  growth direction always has the highest thermal conductivity. Since experimental groups have recently grown diamond nanowires, it will be interesting to see if this prediction is correct.