  Dusty star-forming galaxies at high redshift (1 < z < 3) represent the most
intense star-forming regions in the Universe. Key aspects to these processes
are the gas heating and cooling mechanisms. Although it is well known that
these galaxies are gas-rich, little is known about the gas excitation
conditions. Here we examine these processes in a sample of 24 strongly lensed
star-forming galaxies identified by the \textit{Planck} satellite (LPs) at z ~
1.1 - 3.5. We analyze 162 CO rotational transitions (ranging from Jupper = 1 -
12) and 37 atomic carbon fine-structure lines ([CI]) in order to characterize
the physical conditions of the gas in sample of LPs. We simultaneously fit the
CO and [CI] lines, and the dust continuum emission, using two different
non-LTE, radiative transfer models. The first model represents a two component
gas density, while the second assumes a turbulence driven log-normal gas
density distribution. These LPs are among the most gas-rich, infrared (IR)
luminous galaxies ever observed ($\mu_{\rm L}$L$_{\rm IR(8-1000\mu m) } \sim
10^{13-14.6} $\Lsun; $< \mu_{\rm L}$M$_{\rm ISM}> = 2.7 \pm 1.2 \times 10^{12}$
\Msun, with $\mu_{\rm L} \sim 10-30$ the average lens magnification factor).
Our results suggest that the turbulent ISM present in the LPs can be
well-characterized by a high turbulent velocity dispersion ($<\Delta V_{\rm
turb}> \sim 100 $ \kms) and gas kinetic temperature to dust temperature ratios
$<T_{\rm kin}$/$T_{\rm d}> \sim 2.5$, sustained on scales larger than a few
kpc. We speculate that the average surface density of the molecular gas mass
and IR luminosity $\Sigma_{\rm M_{\rm ISM}}$ $\sim 10^{3 - 4}$ \Msun pc$^{-2}$
and $\Sigma_{\rm L_{\rm IR}}$ $\sim 10^{11 - 12}$ \Lsun kpc$^{-2}$, arise from
both stellar mechanical feedback and a steady momentum injection from the
accretion of intergalactic gas.
