  We study the full distribution of quantum work in generic, noninteracting,
disordered fermionic nanosystems at finite temperature. We derive an analytical
determinant formula for the characteristic function of work statistics for
quantum quenches starting from a thermal initial state. For work small compared
to the thermal energy of the Fermi gas, work distribution is Gaussian, and the
variance of work is proportional to the average work, while in the low
temperature or large work limit, a non-Gaussian distribution with
superdiffusive work fluctuations is observed. Similarly, the time dependence of
the probability of adiabaticity crosses over from an exponential to a stretched
exponential behavior. For large enough average work, the work distribution
becomes universal, and depends only on the temperature and the mean work. Apart
from initial low temperature transients, work statistics are well captured by a
Markovian energy-space diffusion process of hard-core particles, starting from
a thermal initial state. Our findings can be verified by measurements on
nanoscale circuits or via single qubit interferometry.
