  Let a general quantum many-body system at a low temperature adiabatically
cross through the vicinity of the system's quantum critical point. We show that
the system's temperature is significantly suppressed due to both the entropy
majorization theorem in quantum information science and the entropy
conservation law in adiabatic processes. We take the one-dimensional
transverse-field Ising model and spinless fermion system as concrete examples
to show that the inverse temperature might become divergent around their
critical points. Since the temperature is a measurable quantity in experiments,
our work, therefore, provides a practicable proposal to detect quantum phase
transitions.
