  The AC Stark shift induced by blackbody radiation is a major source of
systematic uncertainty in present-day cesium microwave frequency standards. The
shift is parametrized in terms of a third-order electric polarizability
$\alpha_0^{(3)}$ that can be inferred from the static electric field
displacement of the clock transition resonance. In this paper, we report on an
all-optical CPT pump-probe experiment measuring the differential polarizability
$\Delta \alpha_0^{(3)} = \alpha_0^{(3)}(F{=}4) - \alpha_0^{(3)}(F{=}3)$ on a
thermal Cs atomic beam, from which we infer $ \alpha_0^{(3)}(F{=}4) =
2.023(6)_{stat}(9)_{syst}~Hz/(kV/cm)^2$, which corresponds to a scalar Stark
shift parameter $ k_{s} = -2.312(7)_{stat}(10)_{syst}~Hz/(kV/cm)^2$. The result
agrees within two standard deviations with a recent measurement in an atomic
fountain, and rules out another recent result obtained in a Cs vapor cell.
