ABSTRACT The structure and composition of the crust of neutron stars plays an important role in their thermal and magnetic evolution, hence in setting their observational properties. One way to study the properties of the crust of a neutron star, is to measure how it cools after it has been heated during an accretion outburst in a low-mass X-ray binary (LMXB). Such studies have shown that there is a tantalizing source of heat, of currently unknown origin, that is located in the outer layers of the crust and has a strength that varies between different sources and different outbursts. With the aim of understanding the mechanism behind this ‘shallow heating’, we present Chandra and Swift observations of the neutron star LMXB Aql X-1, obtained after its bright 2016 outburst. We find that the neutron star temperature was initially much lower, and started to decrease at much later time, than observed after the 2013 outburst of the source, despite the fact that the properties of the two outbursts were very similar. Comparing our data to thermal evolution simulations, we infer that the depth and magnitude of shallow heating must have been much larger during the 2016 outburst than during the 2013 one. This implies that basic neutron star parameters that remain unchanged between outbursts do not play a strong role in shallow heating. Furthermore, it suggests that outbursts with a similar accretion morphology can give rise to very different shallow heating. We also discuss alternative explanations for the observed difference in quiescent evolution after the 2016 outburst.