We analyze the short-time behavior of the heat and charge currents through nanoscale conductors exposed to a temperature gradient. To this end, we employ Luttinger's thermomechanical potential to simulate a sudden change of temperature at one end of the conductor. We find that the direction of the charge current through an impurity is initially opposite to the direction of the charge current in the steady-state limit. Furthermore, we investigate the transient propagation of energy and particle density driven by a temperature variation through a conducting nanowire. Interestingly, we find that the velocity of the wavefronts of, both, the particle and the energy wave have the same constant value, insensitive to changes in the average electronic density. In the steady-state regime, we find that, at low temperatures, the local temperature and potential, as measured by a floating probe lead, exhibit characteristic oscillations due to quantum interference, with a periodicity that corresponds to half the Fermi wavelength of the electrons.