Abstract: The inverse heat conduction problem (IHCP) is a severely ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. But now the results on inverse heat conduction problem are mainly devoted to the standard inverse heat conduction problem. Some optimal error bounds in a Sobolev space of regularized approximation solutions for a sideways parabolic equation, i.e., a non-standard inverse heat conduction problem with convection term which appears in some applied subject are given.