It is well known that the Boltzmann equation and the incompressible Navier–Stokes equations are well posed in different classes of critical spaces. However, such a rigorous connection in the hydrodynamic limit has not yet been established. In this paper, we rigorously justify the incompressible Navier–Stokes–Fourier limit of the Boltzmann equation with Grad’s angular cutoff in critical hybrid Besov spaces, where the low-frequency regularity is of Fujita–Kato type, while the high frequencies are taken in the spatially critical Besov space embedded into the class of continuous functions. As the Knudsen number tends to zero, the low-frequency modes become dominant, while the high-frequency modes vanish. Moreover, we prove the uniform-in-time strong convergence in the hydrodynamic limit for ill-prepared initial data, with explicit convergence rates.