  Low-dimensional quantum magnets at finite temperatures present a complex
interplay of quantum and thermal fluctuation effects in a restricted phase
space. While some information about dynamical response functions is available
from theoretical studies of the one-triplet dispersion in unfrustrated chains
and ladders, little is known about the finite-temperature dynamics of
frustrated systems. Experimentally, inelastic neutron scattering studies of the
highly frustrated two-dimensional material SrCu$_2$(BO$_3$)$_2$ show an almost
complete destruction of the one-triplet excitation band at a temperature only
1/3 of its gap energy, accompanied by strong scattering intensities for
apparent multi-triplet excitations. We investigate these questions in the
frustrated spin ladder and present numerical results from exact diagonalization
for the dynamical structure factor as a function of temperature. We find
anomalously rapid transfer of spectral weight out of the one-triplet band and
into both broad and sharp spectral features at a wide range of energies,
including below the zero-temperature gap of this excitation. These features are
multi-triplet bound states, which develop particularly strongly near the
quantum phase transition, fall to particularly low energies there, and persist
to all the way to infinite temperature. Our results offer valuable insight into
the physics of finite-temperature spectral functions in SrCu$_2$(BO$_3$)$_2$
and many other highly frustrated spin systems.
