Large eddy simulations (LES) of combustion instabilities are often performed with simplified thermal wall boundary conditions, typically adiabatic walls. However, wall temperatures directly affect the gas temper- atures and therefore the sound speed field. They also control the flame itself, its stabilization characteris- tics and its response to acoustic waves, changing the flame transfer functions (FTFs) of many combustion chambers. This paper presents an example of LES of turbulent flames fully coupled to a heat conduc- tion solver providing the temperature in the combustor walls. LES results obtained with the fully coupled approach are compared to experimental data and to LES performed with adiabatic walls for a swirled turbulent methane/air burner installed at Engler-Bunte-Institute, Karlsruhe Institute of Technology and German Aerospace Center (DLR) in Stuttgart. Results show that the fully coupled approach provides rea- sonable wall temperature estimations and that heat conduction in the combustor walls strongly affects both the mean state and the unstable modes of the combustor. The unstable thermoacoustic mode ob- served experimentally at 750 Hz is captured accurately by the coupled simulation but not by the adiabatic one, suggesting that coupling LES with heat conduction solvers within combustor walls may be necessary in other configurations in order to capture flame dynamics.