  We investigate the first law of thermodynamics in the stationary axisymmetric
configurations composed of two Kerr black holes separated by a massless strut.
Our analysis employs the recent results obtained for the extended double-Kerr
solution and for thermodynamics of the static single and binary black holes. We
show that, similar to the electrostatic case, in the stationary binary systems
the thermodynamic length $\ell$ is defined by the formula
$\ell=L\exp(\gamma_0)$, where $L$ is the coordinate length of the strut, and
$\gamma_0$ is the value of the metric function $\gamma$ on the strut.
