  We study C70 fullerene matter waves in a Talbot-Lau interferometer as a
function of their temperature. While the ideal fringe visibility is observed at
moderate molecular temperatures, we find a gradual degradation of the
interference contrast if the molecules are heated before entering the
interferometer. A method is developed to assess the distribution of the
micro-canonical temperatures of the molecules in free flight. This way the
heating-dependent reduction of interference contrast can be compared with the
predictions of quantum theory. We find that the observed loss of coherence
agrees quantitatively with the expected decoherence rate due to the thermal
radiation emitted by the hot molecules.
