  We report on the thermoelectric power $S(T)$, electrical resistivity and
thermal conductivity measurements on the antiferromagnetic CeCoAl$_4$ compound.
The N\'eel temperature of CeCoAl$_4$ is $T_N$=13.5K and a metamagnetic-like
transition occurs in the magnetic field of about 7.5T. We show that the
magnetic contribution to the thermoelectric power, $S_f(T)$, exhibits a large
peak due to the crystal electric field (CEF) at about 240K and a small anomaly
around the ordering temperature. Surprisingly, the CEF related $S_f(T)$ peak is
close to the upper CEF excitation energy $\Delta_2$=202K, in contrast to the
usual case of the peak position being a fraction of the real CEF excitation.
The applicability of different theoretical and phenomenological models
describing the temperature dependence of the Seebeck effect $S_f(T)$ has been
tested and finally a calculation is proposed, which incorporates a full CEF
levels scheme. For the nonmagnetic reference compound, LaCoAl$_4$, the
thermoelectric power measurements provide an evidence of the phonon drag
contribution, which is not present or masked in the case of CeCoAl$_4$.
