The topological three-dimensional Dirac semimetal ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$ has drawn great attention for the novel physics and promising applications in optoelectronic devices operating in the infrared and terahertz (THz) regimes. Among the extensive studies in the past decades, one intriguing debate is the underlined mechanism governing the nonequilibrium carrier dynamics following photoexcitation. In this study, the temperature-dependent photocarrier dynamics in ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$ film has been investigated with time-resolved terahertz spectroscopy. The experimental results demonstrate that photoexcitation results in abrupt increase in THz photoconductivity, and the subsequent relaxation shows a single exponential relaxation for various temperatures and pump fluences. The relaxation time increases from 4.7 ps at 5 K to 7.5 ps at 220 K, while the lifetime remains almost constant at $\ensuremath{\sim}7.5$ ps with temperature above 220 K. A Rothwarf-Taylor model was employed to fit the temperature-dependent relaxation time, and a narrow energy gap of $\ensuremath{\sim}35\ifmmode\pm\else\textpm\fi{}6$ meV is obtained, which occurs around the Dirac node. Our THz spectroscopy results demonstrate that the photocarrier relaxation in ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$ shows a semiconductorlike behavior, rather than hot-carrier scatterings in graphene and most of metals.