This paper reports on the quantification of the heating induced by nanosecond repetitively pulsed (NRP) glow discharges on a lean premixed methane-air flame. The flame, obtained at room temperature and atmospheric pressure, has an M-shape morphology. The equivalence ratio is 0.95 and the thermal power released by the flame is 113 W. The NRP glow discharges are produced by high voltage pulses of 10 ns duration, 7 kV amplitude, applied at a repetition frequency of 10 kHz. The average power of the plasma, determined from current and voltage measurements, is 1 W, i.e. about 0.9 % of the thermal power of the flame. Broadband vibrational coherent anti-Stokes Raman spectroscopy of nitrogen is used to determine the temperature of the flame with and without plasma enhancement. The temperature evolution in the flame area shows that the thermal impact of NRP glow discharges is in the uncertainty range of the technique, i.e., +/- 40 K.