An initial-boundary value problem for 1D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is thermodynamically perfect and polytropic. Assuming that the initial data are Hölder continuous on 0, 1 and transforming the original problem into homogeneous one, we prove that the state function is Hölder continuous on 0, 1 × 0, T , for each T > 0. The proof is based on a global-in-time existence theorem obtained in the previous research paper and on a theory of parabolic equations.