Variability studies have proven to be a powerful diagnostic tool for understanding the physics and properties of active galactic nuclei (AGNs). They provide insights into the spatial and temporal distribution of the emitting regions, the structure and dynamics of the accretion disc, and the properties of the central black hole. Here, we have analysed the K-band spectral variability of the Seyfert 1.9/2 galaxy NGC 4388 spanning five epochs over a period of 10 yr. We have performed spectral synthesis of the nuclear region and found that the contribution of warm dust (T ~ 800 K) declined by 88 per cent during these 10 yr. In the same period, the [Ca VIII] coronal line decreased 61 per cent, whereas Br γ emission declined 35 per cent. For the He I and H2, we did not detect any significant variation beyond their uncertainties. Based on the time span of these changes, we estimate that the region where the warm dust is produced is smaller than 0.6 pc, which suggests that this spectral feature comes from the innermost part of the region sampled, directly from the AGN torus. On the other hand, the bulk of [Ca VIII] is produced in the inner ~2 pc and the nuclear Br γ region is more extended, spanning a region larger than 3 pc. Lastly, He I and H2 are even more external, with most of the emission probably being produced in the host galaxy rather than in the AGN. This is the first spectroscopic variability study in the near-infrared for an AGN where the central source is not directly visible.