Using a theoretical model, we track the thermal evolution of a cooling neutron star crust after an accretion induced heating period with the goal of constraining the crustal parameters. We present for the first time a crust cooling model $-text{ } NSCooltext{ } -$ that takes into account detailed variability during the full outburst based on the observed light curve. We apply our model to KS 1731-260. The source was in outburst for $sim$12 years during which it was observed to undergo variations on both long (years) and short (days-weeks) timescales. Our results show that KS 1731-260 does not reach a steady state profile during the outburst due to fluctuations in the derived accretion rate. Additionally, long time-scale outburst variability mildly affects the complete crust cooling phase, while variations in the final months of the outburst strongly influence the first $sim$40 days of the calculated cooling curve. We discuss the consequences for estimates of the neutron star crust parameters, and argue that detailed modelling of the final phase of the outburst is key to constraining the origin of the shallow heat source.
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