The surfaces of perovskite oxides affect their functional properties, and while a bulk-truncated (1$times$1) termination is generally assumed, its existence and stability is controversial. Here, such a surface is created by cleaving the prototypical SrTiO$_3$(001) in ultra-high vacuum, and its response to thermal annealing is observed. Atomically resolved nc-AFM shows that intrinsic point defects on the as-cleaved surface migrate at temperatures above 200,$^circ$C. At 400--500,$^circ$C, a disordered surface layer forms, albeit still with a (1$times$1) pattern in LEED. Purely TiO$_2$-terminated surfaces, prepared by wet-chemical treatment, are also disordered despite their (1$times$1) periodicity in LEED.
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