  We study heating and heat dissipation of a single \c60 molecule in the
junction of a scanning tunneling microscope (STM) by measuring the electron
current required to thermally decompose the fullerene cage. The power for
decomposition varies with electron energy and reflects the molecular resonance
structure. When the STM tip contacts the fullerene the molecule can sustain
much larger currents. Transport simulations explain these effects by molecular
heating due to resonant electron-phonon coupling and molecular cooling by
vibrational decay into the tip upon contact formation.
