  We theoretically and numerically investigate the temperature-dependent
properties of the biphotons generated from four isomorphs of periodically poled
$\mathrm{KTiOPO_4}$ (PPKTP): i.e., PPRTP, PPKTA, PPRTA and PPCTA. It is
discovered that the first type of group-velocity-matched (GVM) wavelength is
decreased by 6.4, 1.2, 8.9, 25.6 and 6.3 nm, while the phase-matched wavelength
is decreased by 4.4, -0.4, -1.2, 29.1 and 59.5 nm for PPKTP, PPRTP, PPKTA,
PPRTA and PPCTA, respectively, when the temperature is increased from
20$\,^{\circ}\mathrm{C}$ to 120$\,^{\circ}\mathrm{C}$. Although the maximal
spectral purity of the heralded single photons is not changed at different
temperature, the Hong-Ou-Mandel (HOM) interference shows different patterns due
to a shift of the joint spectral amplitude. These thermal effects are very
important for precise control of the quantum state for the future applications
in quantum information processing, for example, in quantum interference or
spectroscopy.
