It is well known that an n × n Wishart matrix with d degrees of freedom is close to the appropriately centered and scaled Gaussian Orthogonal Ensemble (GOE) if d is large enough. Recent work of Bubeck, Ding, Eldan, and Racz, and independently Jiang and Li, shows that the transition happens when d = Θ(n 3 ). Here we consider this critical window and explicitly compute the total variation distance between the Wishart and GOE matrices when d/n 3 → c ∈ (0, ∞). This shows, in particular, that the phase transition from Wishart to GOE is smooth. * Microsoft Research; miracz@microsoft.com.