We report on a detailed study of the spectral and temporal properties of the neutron star low mass X-ray binary SLX 1737-282, which is located only ~1degr away from Sgr A. The system is expected to have a short orbital period, even within the ultra-compact regime, given its persistent nature at low X-ray luminosities and the long duration thermonuclear burst that it has displayed. We have analysed a Suzaku (18 ks) observation and an XMM-Newton (39 ks) observation taken 7 years apart. We infer (0.5-10 keV) X-ray luminosities in the range 3-6 x10^35erg s-1, in agreement with previous findings. The spectra are well described by a relatively cool (kTbb = 0.5 keV) black body component plus a Comptonized emission component with {Gamma} ~1.5-1.7. These values are consistent with the source being in a faint hard state, as confirmed by the ~ 20 per cent fractional root mean square amplitude of the fast variability (0.1 - 7 Hz) inferred from the XMM-Newton data. The electron temperature of the corona is >7 keV for the Suzaku observation, but it is measured to be as low as ~2 keV in the XMM-Newton data at higher flux. The latter is significantly lower than expected for systems in the hard state. We searched for X-ray pulsations and imposed an upper limit to their semi-amplitude of 2 per cent (0.001 - 7 Hz). Finally, we investigated the origin of the low frequency variability emission present in the XMM-Newton data and ruled out an absorption dip origin. This constraint the orbital inclination of the system to 65 degr unless the orbital period is longer than 11 hr (i.e. the length of the XMM-Newton observation).
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