  We study a Brownian Carnot cycle introduced by T. Schmiedl and U. Seifert
[Europhys. Lett. \textbf{81}, 20003 (2008)] from a viewpoint of the linear
irreversible thermodynamics. By considering the entropy production rate of this
cycle, we can determine thermodynamic forces and fluxes of the cycle and
calculate the Onsager coefficients for general protocols, that is, arbitrary
schedules to change the potential confining the Brownian particle. We show that
these Onsager coefficients contain the information of the protocol shape and
they satisfy the tight-coupling condition irrespective of whatever protocol
shape we choose. These properties may give an explanation why the
Curzon-Ahlborn efficiency often appears in the finite-time heat engines.
