  This paper establishes the precise small-time asymptotic behavior of the
spectral heat content for isotropic L\'evy processes on bounded $C^{1,1}$ open
sets of $\mathbb{R}^{d}$ with $d\ge 2$, where the underlying characteristic
exponents are regularly varying at infinity with index $\alpha\in (1,2]$,
including the case $\alpha=2$. Moreover, this asymptotic behavior is shown to
be stable under an integrable perturbation of its L\'evy measure. These results
cover a wide class of isotropic L\'evy processes, including Brownian motions,
stable processes, and jump diffusions, and the proofs provide a unified
approach to the asymptotic behavior of the spectral heat content for all of
these processes.

Probability