The flame in a gas turbine model combustor close to blow-off is studied using large eddy simulation with the objective of investigating the sensitivity of including different heat loss effects within the modelling. A presumed joint probability density function approach based on the mixture fraction and progress variable with unstrained flamelets is used. The normalised enthalpy is included in the probability density function to account for heat loss within the flame. Two simulations are presented that use fixed temperature boundary conditions, and use adiabatic and non-adiabatic formulations of the combustion model. The results are compared against the previous fully adiabatic case and experimental data. The statistics for the simulations are similar to the results obtained from the fully adiabatic case. Improved statistics are obtained for the temperature in the near-wall regions. The non-adiabatic flamelet case shows the average reaction rate values at the flame root are approximately 50% smaller in comparison to the adiabatic flamelet cases. This causes the lift-off height to be overestimated. The time series of the lift-off height and the volume integrated heat release rate show that including non-adiabatic flamelets causes the flame to be highly unstable. A higher enthalpy deficit is seen in the near-field regions when the flame root is not present and experiencing some lift-off, suggesting that the flame is more dynamic when including heat loss.