  At finite temperatures, the quantum critical region (QCR) emerges as a
consequence of the interplay between thermal and quantum fluctuations. We seek
for suitable physical quantities, which during dynamics can give prominent
response to QCR in the transverse field quantum $XY$ model. We report that the
maximum energy absorbed, the nearest neighbor entanglement and the quantum
mutual information of the time evolved state after a quench of the transverse
magnetic field exhibits a faster fall off with temperature when the initial
magnetic field is taken from within the QCR, compared to the choice of the
initial point from different phases. We propose a class of dynamical
quantifiers, originated from the response of these physical quantities and show
that they can faithfully mimic the equilibrium physics, namely detection of the
QCR at finite temperatures.
