  We present new CO ($J=5-4$ and $7-6$) and [CI] ($^3P_2\,-\, ^3P_1$ and
$^3P_1\,-\, ^3P_0$) emission line observations of the star-forming galaxy D49
at the massive end of the Main Sequence at $z=3$. We incorporate previous CO
($J=3-2$) and optical-to-millimetre continuum observations to fit its spectral
energy distribution (SED). Our results hint at high-$J$ CO luminosities
exceeding the expected location on the empirical correlations with the infrared
luminosity. [CI] emission fully consistent with the literature trends is found.
We do not retrieve any signatures of a bright active galactic nucleus that
could boost the $J=5-4,\,7-6$ lines in either the infrared or X-ray bands, but
warm photon-dominated regions, shocks or turbulence could in principle do so.
We suggest that mechanical heating could be a favourable mechanism able to
enhance the gas emission at fixed infrared luminosity in D49 and other
main-sequence star-forming galaxies at high redshift, but further investigation
is necessary to confirm this explanation. We derive molecular gas masses from
dust, CO, and [CI] that all agree within the uncertainties. Given its large
star formation rate (SFR) $\sim 500~M_\odot~{\rm yr}^{-1}$ and stellar mass
$>10^{11.5}~M_\odot$, the short depletion time scale of $<0.3$ Gyr might
indicate that D49 is experiencing its last growth spurt and will soon transit
to quiescence.
