Conjugate heat transfer is gaining acceptance for predicting the thermal loading in high pressure nozzles. Despite the accuracy nowadays of numerical solvers, it is not clear how to include the uncertainties associated to the turbulence level, the temperature distribution, or the thermal barrier coating thickness in the numerical simulations. All these parameters are stochastic even if their value is commonly assumed to be deterministic. For the first time, in this work a stochastic analysis is used to predict the metal temperature in a real high-pressure nozzle. The domain simulated is the high pressure nozzle of an F-type Mitsubishi Heavy Industries gas turbine. The complete coolant system is included: impingement, film, and trailing edge cooling. The stochastic variations are included by coupling uncertainty quantification methods and conjugate heat transfer. Two uncertainty quantification methods have been compared: a probabilistic collocation method (PCM) and a stochastic collocation method (SCM). The stochastic distribution of thermal barrier coating thickness, used in the simulations, has been measured at the midspan. A Gaussian distribution for the turbulence intensity and hot core location has been assumed. By using PCM and SCM, the probability to obtain a specific metal temperature at midspan is evaluated. The two methods predict the same distribution of temperature with a maximum difference of 0.6%, and the results are compared with the experimental data measured in the real engine. The experimental data are inside the uncertainty band associated to the CFD predictions. This work shows that one of the most important parameters affecting the metal temperature uncertainty is the pitch-wise location of the hot core. Assuming a probability distribution for this location, with a standard deviation of 1.7 deg, the metal temperature at midspan can change up to 30%. The impact of turbulence level and thermal barrier coating thickness is 1 order of magnitude less important.