  We develop a theory to describe energy relaxation of photo-excited carriers
in low-temperature ordered states with band gap opening and formulate carrier
relaxation time $\tau$ near and below transition temperature $T_{\mathrm{c}}$
by quantifying contributions from different carrier-phonon scatterings to the
relaxation rate. The theory explains anomalous experimental observations of
$\tau$ in gapped systems. Transverse acoustic (TA) phonon modes play a crucial
role in carrier relaxation; their heat capacity determines $\tau$-divergence
near $T_{\mathrm{c}}$. The theory is validated by fitting $\tau$ of fullerene
polymers onto a theoretical curve.
