We use model simulations from the CESM1-CAM5-BGC-LE dataset to characterise the Arctic sea ice thickness internal variability both spatially and temporally. These properties, and their stationarity, are investigated in three different contexts: (1) constant pre-industrial, (2) historical and (3) projected conditions. Spatial modes of variability show highly stationary patterns regardless of the forcing and mean state. A temporal analysis reveals two peaks of significant variability, and despite a non-stationarity on short timescales, they remain more or less stable until the first half of the 21st century, where they start to change once summer ice-free events occur, after 2050.