We report highly localized second-order fibre Bragg gratings at 1585 nm inscribed by point-by-point focused infrared femtosecond pulses. A thin gold coating deposited on the fibre outer surface at the grating location allows shielding the cladding mode resonances from the outer medium, so that they remain present in the transmitted amplitude spectrum. The Bragg resonance of the second-order grating is surrounded by high-order cladding mode resonances of the firstorder grating. These cladding modes exhibit the same temperature sensitivity as the Bragg resonance (10.6 pm/°C) but high differential strain sensitivity (-0.55 pm/µε versus 1.20 pm/µε for the Bragg mode). Therefore, the conditioning of the matrix inversion as demodulation method is fully satisfied, yielding a new design of fibre sensor able to discriminate between temperature and strain, with an unprecedented sensitivity.Keywords: localized fibre Bragg grating, femtosecond IR inscription technique, strain and temperature sensitivities, temperature and strain sensor, temperature and strain discrimination method.