  The zero crossing of the dynamic differential scalar polarizability of the
$S_{1/2}-D_{5/2}$ clock transition in $^{138}$Ba$^+$ has been determined to be
$459.1614(28)\,$THz. Together with previously determined matrix elements and
branching ratios, this tightly constrains the dynamic differential scalar
polarizability of the clock transition over a large wavelength range ($\gtrsim
700\,$nm). In particular it allows an estimate of the blackbody radiation shift
of the clock transition at room temperature.
