  We study the large-time and small-time asymptotic behaviors of the spectral
heat content for time-changed stable processes, where the time change belongs
to a large class of inverse subordinators. For the large-time behavior, the
spectral heat content decays polynomially with the decay rate determined by the
Laplace exponent of the underlying subordinator, which is in sharp contrast to
the exponential decay observed in the case when the time change is a
subordinator. On the other hand, the small-time behavior exhibits three
different decay regimes, where the decay rate is determined by both the Laplace
exponent and the index of the stable process.
