Flat adiabatic stretchless methane/air flames at atmospheric pressure are investigated with CARS thermometry in a folded BOXCARS configuration. The flames are stabilized on a perforated-plate burner by adjusting the flow until zero net heat flux to the burner is created. Vertical temperature profiles are measured in flames with equivalence ratios of 0,80, 0.90, 1,00, and 1.10, up to a height of 35.0 mm above the burner. One horizontal profile is measured in the flame with phi = 0.80. The measurements are compared with calculations of free flames, based on the GRI2.11 reaction mechanism. A simple model is implemented to account for radiative losses of the flame. A good agreement is found between the calculations and the measurements in the preheating zone and the flame front, as well as in the downstream region, It can be concluded that the heat flux burner provides well-defined adiabatic flames which can be used as reference flames for other (laser-based) measurement techniques.