As far as the preliminary thermal design of gas turbine components is concerned, 1-D codes are still widely used in standard industrial practice. Among the different components, the combustor is one of the most critical ones and its thermal design still greatly affects the reliability and life of the entire engine. During the initial phases of the design process, parameters are often roughly known. For this preliminary phase, a low-order approach is preferred instead of a high-fidelity simulation: the exploration of the whole space is extremely important to better understand the behavior of the system and to focus on the design objectives. Uncertainty quantification (UQ) methods, mainly developed in recent years and applied in many fields, are useful tools for the preliminary design phase and provide support during the whole design process. The objective of this work is to estimate the main sources of uncertainties in the design phase of an aeroengine effusion cooled combustor. The test case is based on a full annular lean-burn combustor, tested during the LEMCOTEC (Low EMissions COre-engine TEChnologies) European project. Among the test points investigated in the experimental campaign, the Approach condition is here analyzed. The inner liner is taken into consideration to investigate the metal temperature. Therm-1D, a 1-D in-house simulation code, is used to model the combustor and the open-source tool DAKOTA is adopted for the uncertainty quantification analysis. The baseline case of the combustor is studied and several uncertainty analyses are investigated. They are divided into 3 main groups: geometrical, tuning modelling parameters and thermal loads. For each group, the most relevant parameters are considered as a source of input uncertainty. In particular, a classical Monte Carlo approach is compared with four innovative polynomial-chaos approaches for each group: Gauss quadrature, total order with LHS sampling, stochastic collocation, and Smolyak. The analyses proved how the last two methods give the best results with a sensible lower amount of simulation (depending on the number of input variables). Lastly, results are compared with experimental data to achieve a better understanding of the most relevant input parameters and the propagation of their uncertainty on the results.