  We study heat fluctuations in the two-time measurement framework. For bounded
perturbations, we give sufficient ultraviolet regularity conditions on the
perturbation for the moments of the heat variation to be uniformly bounded in
time, and for the Fourier transform of the heat variation distribution to be
analytic and uniformly bounded in time in a complex neighborhood of 0. On a set
of canonical examples, with bounded and unbounded perturbations, we show that
our ultraviolet conditions are essentially necessary. If the form factor of the
perturbation does not meet our assumptions, the heat variation distribution
exhibits heavy tails. The tails can be as heavy as preventing the existence of
a fourth moment of the heat variation.
