Role of a boundary in the relationship between black hole temperature and the trace anomaly

For a black hole surrounded by a massless reflecting shell the quantum correction to temperature caused by the back reaction of Hawking radiation is calculated. The correction is expressed in terms of the trace of the total stress-energy tensor including the shell contribution and for a massless field proves to be proportional to the pressure at the shell surface. It is shown that because of the shell the correction remains nonzero even in field theories without conformal anomalies. The shell contribution dominates at large distances where for a given total mass it makes the correction positive irrespective of a field species.