  This paper establishes the small-time asymptotic behaviors of the regular
heat content and spectral heat content for general Gaussian processes in both
one-dimensional and multi-dimensional settings, where the boundary of the
underlying domain satisfies some smoothness condition. For the amount of heat
loss associated with the spectral heat content, the exact asymptotic behavior
with rate function being the expected supremum process is obtained, whereas for
the regular heat content, the exact asymptotic behavior is described in terms
of the standard deviation function.
