We monitored the neutron star low-mass X-ray binary SAX J1750.8-2900 after the end of its 2015/2016 outburst using the X-ray Telescope (XRT) aboard Swift to detect possible post-outburst rebrightenings, similar to those seen after its 2008 outburst. We did not detect any rebrightening behaviour, suggesting that the physical mechanism behind the rebrightening events is not always active after each outburst of the source. Any model attempting to explain these rebrightenings should thus be able to reproduce the different outburst profiles of the source at different times. Surprisingly, our Swift/XRT observations were unable to detect the source, contrary to previous Swift/XRT observations in quiescence. We determined a temperature upper limit of $leq$ 106 eV, much colder than the post 2008 outburst value of $sim$ 145 eV. We also report on an archival Chandra observation of the source after its 2011 outburst and found a temperature of $sim$ 126 eV. These different temperatures, including the non-detection very close after the end of the 2015/2016 outburst, are difficult to explain in any model assuming we observe the cooling emission from a neutron star core or an accretion-heated crust. We discuss our observations in the context of a change in envelope (the outer $sim$ 100 m of the crust) composition and (possibly in combination with) a cooling crust. Both hypotheses cannot explain our results unless potentially unrealistic assumptions are made. Irrespective of what causes the temperature variability, it is clear that the neutron star in SAX J1750.8-2900 may not be as hot as previously assumed.
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