The transient neutron star low-mass X-ray binary EXO 1745−248, located in the globular cluster Terzan 5, was detected during its quiescent state with Chandra in 2003. The source displayed a 0.5-10 keV quiescent X-ray luminosity of L q∼ 1033 (D/5.5 kpc)2 erg s−1, which was completely dominated by hard non-thermal emission. This is at odds with other non-pulsating neutron stars that typically show detectable soft thermal emission at such quiescent luminosities. Here we use three additional Chandra observations, performed in 2009 and 2011, to further study the quiescent properties of EXO 1745−248. We find that the power-law intensity varies considerably up to a factor of ∼3 within hours and by about one order of magnitude between the different epochs. We discuss the implications of the observed change in quiescent flux for the interpretation of the hard power-law emission. We constrain the neutron star surface temperature as seen by a distant observer to kT ∞≲ 42 eV and the thermal bolometric luminosity to L th q, bol≲ 7 × 1031 (D/5.5 kpc)2 erg s−1. This confirms that EXO 1745−248 harbours a relatively cold neutron star and suggests that, for example, enhanced cooling mechanisms are operating in the stellar core or that the binary on average resides in quiescence for hundreds of years.