  We present a detailed study of the absolute Doppler-broadened absorption of a
probe beam scanned across the potassium D lines in a thermal vapour. Spectra
using a weak probe were measured on the 4S $\rightarrow$ 4P transition and
compared to the theoretical model of the electric susceptibility detailed by
Zentile et al. (2015) in the code named ElecSus. Comparisons were also made on
the 4S $\rightarrow$ 5P transition with an adapted version of ElecSus. This is
the first experimental test of ElecSus on an atom with a ground state hyperfine
splitting smaller than that of the Doppler width. An excellent agreement was
found between ElecSus and experimental measurements at a variety of
temperatures with rms errors of $\sim 10^{-3}$. We have also demonstrated the
use of ElecSus as an atomic vapour thermometry tool, and present a possible new
measurement technique of transition decay rates which we predict to have a
precision $\sim$ 3 kHz.
