Advanced military gas turbine combustors, such as those for the Joint Strike Fighter (JSF), are running at very high fuel-air ratios at full power, approaching stoichiometric conditions. In these combustors, unmixedness at the combustor exit can easily result in fuel-rich pockets with high levels of carbon monoxide (CO) and hydrogen (H2). These species can interact with the turbine inlet guide vane cooling airflow and release heat near the vane surface. Thus, instead of cooling the vane, cooling airflow can actually increase vane temperatures, resulting in reduced life and even catastrophic damage. To model this environment, new analytical tools are needed. In this paper, calculations from Large Eddy Simulations (LES) of a generic inlet guide vane, currently being studied at the University of Cincinnati's Hot-streak Experimental Facility, are reported. The simulations include the cooling flow internal passages, flow through the cooling holes, the external hot gas flow, and the solid metal (i.e. conjugate heat transfer). Both Reynolds Averaged Navier Stokes (RANS) and LES calculations were performed.