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 electronphonon coupling and molecular cooling by vibrational decay into the tip upon contact formation.The paradigm of molecular electronics is the use of a single molecule as an electronic device [1]. This concept is sustained on the basis that a single molecule (or a molecular thin film) should withstand the flow of electron current densities as large as 10 10 A/m 2 without degrading. A fraction of these electrons heat the molecular junction through inelastic scattering with the molecule [2]. The temperature at the junction is a consequence of an equilibrium between heating due to electron flow and heat dissipation out of the junction. The former is dominated by the coupling of electronic molecular states with molecular vibrons [2,3,4]. The latter depends on the strength of the vibrational coupling between the "hot" molecular vibrons and the bath degrees of freedom of the "cold" electrodes.Theoretical studies predicted that current-induced heating in molecular junctions can be large enough to affect the reliability of molecular devices [2]. However, experimental access to this information is very limited. Recent studies of the thermally activated force during molecular detachment from a lead [5,6] and of structural fluctuation during attachment to it [7] reveal that the temperature of a molecular junction can reach several hundred degrees under normal working conditions, thus revealing that present devices work on the limit of practical operability [8]. Heat dissipation away from the junction becomes an important issue.In this work, we characterize the mechanisms of heating and heat dissipation induced by the flow of current across a single molecule. Our approach is based on detecting the limiting electron current inducing molecular decomposition at varying applied source-drain bias (i.e. the maximum power one molecule can sustain). We use a low temperature scanning tunneling microscope (STM) to control the flow of electrons through a single C 60 molecule at an increasing rate until the molecule decomposes. By comparing the power applied for decomposition (P dec ) in tunneling regime and in contact with the STM tip we find that it depends significantly on two factors: i) P dec decreases when molecular resonances participate in the transport, evidencing that they enhance the heating; ii) P dec increases as the molecule is contacted to the source and drain electrodes, revealing the heat dissipation by phonon coupling to the leads. A good contact between the single-molecule (SM) device and the leads is hence an important requirement for its ope...