  In this paper we study the asymptotic behavior, as $t\downarrow 0$, of the
spectral heat content $Q^{(\alpha)}_{D}(t)$ for isotropic $\alpha$-stable
processes, $\alpha\in [1,2)$, in bounded $C^{1,1}$ open sets $D\subset \R^{d}$,
$d\geq 2$. Together with the results from \cite{Val2017} for $d=1$ and
\cite{GPS19} for $\alpha\in (0,1)$, the main theorem of this paper establishes
the asymptotic behavior of the spectral heat content up to the second term for
all $\alpha\in (0,2)$ and $d\geq1$, and resolves the conjecture raised in
\cite{Val2017}.
