We present a comprehensive characterization of cold molecular beams from a cryogenic buffer-gas cell, providing an insight into the physics of buffer-gas cooling. Cold molecular beams are extracted from a cryogenic cell by electrostatic guiding, which is also used to measure their velocity distribution. Molecules rotational-state distribution is probed via radio-frequency resonant depletion spectroscopy. With the help of complete trajectory simulations, yielding the guiding efficiency for all of the thermally populated states, we are able to determine both the rotational and the translational temperature of the molecules at the output of the buffer-gas cell. This thermometry method is demonstrated for various regimes of buffer-gas cooling and beam formation as well as for molecular species of different sizes, $rm{CH_3F}$ and $rm{CF_3CCH}$. Comparison between the rotational and translational temperatures provides evidence of faster rotational thermalization for the $rm{CH_3F-He}$ system in the limit of low He density. In addition, the relaxation rates for different rotational states appear to be different.
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