  We investigate the loss of adiabaticity when cooling a many-body quantum
system from an initial thermal state toward a quantum critical point. The
excitation density, which quantifies the degree of adiabaticity of the
dynamics, is found to obey scaling laws in the cooling velocity as well as in
the initial and final temperatures of the cooling protocol. The scaling laws
are universal, governed by the critical exponents of the quantum phase
transition. The validity of these statements is shown analytically for a Kitaev
quantum wire coupled to Markovian baths and argued to be valid under rather
general conditions. Our results establish that quantum critical properties can
be probed dynamically at finite temperature, without even varying the control
parameter of the quantum phase transition.
