  Thermal conductivities $\Lambda $ of amorphous carbon thin films are measured
in the temperatures range 80--400 K using the $3\omega $ method. Sample films
range from soft a-C:H prepared by remote-plasma deposition ($\Lambda = 0.20$ W
m$^{-1}$ K$^{-1}$ at room temperature) to amorphous diamond with a large
fraction of $sp^3$ bonded carbon deposited from a filtered-arc source ($\Lambda
= 2.2$ W m$^{-1}$ K$^{-1}$). Effective-medium theory provides a
phenomenological description of the variation of conductivity with mass
density. The thermal conductivities are in good agreement with the minimum
thermal conductivity calculated from the measured atomic density and
longitudinal speed of sound.
