  Two samples of the [Ca$_2$CoO$_{3-t}$]$_{0.62}$(CoO$_2$) misfit cobaltate,
often denoted as the Ca$_{3}$Co$_{3.93}$O$_{9}$ phase, were prepared from the
same ceramic material by the oxygen and argon annealing, resulting in different
carrier concentrations in the conducting CoO$_{2}$ layers, n=0.31 and 0.19
hole/Co, respectively. Electrical and thermal transport properties were studied
in dependence of magnetic field up to 140 kOe. The magnetothermopower data
reveal an extra spin-entropy contribution to Seebeck coefficient that is not
expected for carriers of Fermi liquid character. Its magnitude is
unprecedentedly large and makes at zero field up to 50$\%$ of the theoretical
limit k$_B$/$e$ ln2$ = 59 \mu VK^{-1}$. This spin-entropy contribution is
gradually suppressed with increasing magnetic field, and the saturation is even
observed when temperatures are low enough. To understand the results, the
thermopower is treated in terms of purely thermodynamic Kelvin formula, and
so-called Spin liquid model is evoked, providing a reason for the spin-entropy
manifestation in the [Ca$_2$CoO$_{3-t}$]$_{0.62}$(CoO$_2$) misfits.
