Summary: We revisit the classical work of R. E. Caflisch [Commun. Pure. Appl. Math. 33, 651–666 (1980; Zbl 0424.76060)] for compressible Euler limit of the Boltzmann equation. By using a new \(L^2\)-\(L^\infty\) method, we prove the validity of the Hilbert expansion before shock formations in the Euler system with moderate temperature variation.