Knowing the flow conditions at the combustor turbine interface is a key asset for an efficient cooling design of high-pressure turbines. However, measurements and numerical predictions of combustor exit conditions are challenging due to the extreme temperatures and complex flow patterns in modern combustors. Even the time-averaged flow fields at the combustor exit which are commonly used as inlet condition for simulations of the turbine are therefore subject to uncertainty. The goal of this paper is to illustrate how aleatory uncertainties in the magnitude and position of residual swirl and hot spots at the combustor exit affect uncertainties in the prediction of cooling and heat load of the first nozzle guide vane. Also, it is identified which of these uncertain parameters have the greatest impact. An iso-thermal test rig and an engine realistic setup with lean burn inflow conditions are investigated. The analysis combines a parameterized model for combustor exit flow fields with uncertainty quantification methods. It is shown that the clocking position of turbine inlet swirl has a large effect on the formation of secondary flows on the vane surface and thus affects the uncertainty of thermal predictions on the hub and vanes.