  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.
