  We develop an exact approach to study the quench dynamics of hard-core bosons
initially in thermal equilibrium in one-dimensional lattices. This approach is
used to study the sudden expansion of thermal states after confining potentials
are switched off. We find that a dynamical fermionization of the momentum
distribution occurs at all temperatures. This phenomenon is studied for low
initial site occupations, for which the expansion of the cloud is self-similar.
In this regime, the occupation of the natural orbitals allows one to
distinguish hard-core bosons from noninteracting fermions. We also study the
free expansion of initial Mott insulating domains at finite temperature, and
show that the emergence of off-diagonal one-body correlations is suppressed
gradually with increasing temperature. Surprisingly, the melting of the Mott
domain is accompanied by an effective cooling of the system. We explain this
phenomenon analytically using an equilibrium description based on an emergent
local Hamiltonian.
