  We conduct first-principles theoretical studies to investigate the
temperature-dependent phonon properties of orthorhombic SrZrO$_3$ (SZO)
perovskite. Our calculations include the quasiharmonic approximation, in which
we explored mode Gr\"uneisen parameters, thermal expansion, and frequency
shifts for several optical modes. For most modes these shifts exhibit a
downward trend with increasing temperature, contributing to the normal behavior
of frequencies with temperature. We also studied the temperature dependence of
linewidths and lineshifts for several phonon modes within the third-order
lattice anharmonic effect. The lineshifts for most modes also exhibit a
downward trend with temperature, further supporting the normal
temperature-dependent behavior of phonon modes. However, a few optical modes
display an upward trend in lineshifts with increasing temperature, which in
principle, could lead to anomalous temperature-dependent behavior in their
frequencies. Nevertheless, when we incorporate all corrections, including
quasiharmonic and third-order anharmonic shifts, to the frequencies obtained
within the harmonic approximation, almost all modes exhibit normal behavior
with temperature, displaying blue shifts with cooling.
