  In this paper we continue our program of computing Casimir self-entropies of
idealized electrical bodies. Here we consider an electromagnetic
$\delta$-function sphere ("semitransparent sphere") whose electric
susceptibility has a transverse polarization with arbitrary strength.
Dispersion is incorporated by a plasma-like model. In the strong coupling
limit, a perfectly conducting spherical shell is realized. We compute the
entropy for both low and high temperatures. The TE self-entropy is negative as
expected, but the TM self-entropy requires ultraviolet and infrared
subtractions, and, surprisingly, is only positive for sufficiently strong
coupling. Results are robust under different regularization schemes.
