  This paper studies, by employing analytical tools, the small time behavior of
the heat content for the Poisson kernel over the unit ball in $\Rd$, $d\geq 2$
by working with its related set covariance function. As a result, we obtain a
representation for the third term in the expansion of the heat content over the
unit ball and provide the explicit form of the this term in the particular
cases $d=2$ and $d=3$.
