  This article concerns the Weyl series of spectral functions associated with
the Dirichlet Laplacian in a $d$-dimensional domain with a smooth boundary. In
the case of the heat kernel, Berry and Howls predicted the asymptotic form of
the Weyl series characterized by a set of parameters. Here, we concentrate on
another spectral function, the (normalized) heat content. We show on several
exactly solvable examples that, for even $d$, the same asymptotic formula is
valid with different values of the parameters. The considered domains are
$d$-dimensional balls and two limiting cases of the elliptic domain with
eccentricity $\epsilon$: A slightly deformed disk ($\epsilon\to 0$) and an
extremely prolonged ellipse ($\epsilon\to 1$). These cases include 2D domains
with circular symmetry and those with only one shortest periodic orbit for the
classical billiard. We analyse also the heat content for the balls in odd
dimensions $d$ for which the asymptotic form of the Weyl series changes
significantly.
