Several studies have shown the key role of the rigid unit modes, i.e. rotational motions between neighbouring SiO4 tetrahedra, in glass and in béta-cristobalite due to the disorder generated by the large atomic amplitudes. They do not however reach a conclusion concerning heat conduction. To determine the nature of the heat carriers in the amorphous phase, we carry out an ultrashort timescale analysis of heat transfer in béta-cristobalite ; the behaviour is comparable to that of amorphous silica, as shown by our density of states and heat flux autocorrelation function calculations. We prove that rigid unit modes can be identified as the heat carriers by showing that the thermal relaxation time is in very good agreement with the rigid unit mode relaxation time predicted in the literature. Finally, we provide thermal conductivity data for béta-cristobalite which are not available in the literature.