  We investigate the local electron temperature distribution in carbon
nano-ribbon (CNR) and graphene junctions subject to an applied thermal
gradient. Using a realistic model of a scanning thermal microscope, we predict
quantum temperature oscillations whose wavelength is related to that of Friedel
oscillations. Experimentally, this wavelength can be tuned over several orders
of magnitude by gating/doping, bringing quantum temperature oscillations within
reach of the spatial resolution of existing measurement techniques.
