Ultra high intensity lasers face thermal management issues that limit their repetition rates. The key challenge is to efficiently evacuate the heat deposited in the amplifier by the optical pumping without impacting the output laser beam quality. The amplifier can have a multi-slab geometry where the laser beam crosses successive amplifying slabs and the cooling channels that separate them. The present work investigates numerically how a cryogenic cooling of the amplifier by turbulent channel flows may affect the wavefront of the laser beam. To this end, large eddy simulations (LES) representative of the amplifier cooling are performed using TrioCFD, a code developed by the CEA. First, validation simulations are carried out for heated channel flows, allowing comparisons to direct numerical simulation results from the literature. Then LES of an open turbulent channel flow cooling two slabs are conducted using conjugated heat transfer between the solid and the fluid. The phase distortions, mean and fluctuations, induced by the inhomogeneous and turbulent temperature field are computed directly from the LES. A moderate although non-negligible effect of the turbulence on the laser wavefront was found. This optical effect increases when the slab heating increases. A comparison to the Sutton model, widely used in aero-optic studies, was performed and its applicability was found limited for this problem. For the first time, TrioCFD is used to address the question of the beam impact of the cooling of laser amplifiers, and it has proven to be a valuable tool for such application.