  We employ a recently developed population-orbit superposition technique to
simultaneously fit the stellar kinematic and age maps of 82 CALIFA spiral
galaxies and obtain the ages of stars in different dynamical structures. We
first evaluated the capabilities of this method on CALIFA-like mock data
created from the Auriga simulations. The recovered mean ages of dynamically
cold, warm, and hot components match the true values well, with an
observational error of up to $20\%$ in the mock age maps. For CALIFA spiral
galaxies, we find that the stellar ages of the cold, warm, and hot components
all increase with the stellar mass of the galaxies, from $\overline{t_{\rm
cold}}\sim2.2$ Gyr, $\overline{t_{\rm warm}}\sim2.3$ Gyr, and $\overline{t_{\rm
hot}}\sim2.6$ Gyr for galaxies with stellar mass $M_*<10^{10}\,\rm M_{\odot}$,
to $\overline{t_{\rm cold}}\sim4.0$ Gyr, $\overline{t_{\rm warm}}\sim5.1$ Gyr,
and $\overline{t_{\rm hot}}\sim5.9$ Gyr for galaxies with $M_*>10^{11}\,\rm
M_{\odot}$. About $80\%$ of the galaxies in our sample have $t_{\rm hot}>t_{\rm
cold}$, and the mean values of $t_{\rm hot}-t_{\rm cold}$ also increase with
stellar mass, from $0.7_{-0.2}^{+0.6}$ Gyr in low-mass galaxies ($10^{8.9}\,\rm
M_{\odot}<M_*\le10^{10.5}\,\rm M_{\odot}$) to $1.7_{-0.2}^{+0.7}$ Gyr in
high-mass galaxies ($10^{10.5}\,\rm M_{\odot}<M_*<10^{11.3}\,\rm M_{\odot}$).
The stellar age is younger in disks than in bulges, on average. This suggests
that either the disks formed later and/or that they experienced a more
prolonged and extensive period of star formation. Lower-mass spiral galaxies
have younger bulges and younger disks, while higher-mass spiral galaxies
generally have older bulges, and their disks span a wide range of ages. This is
consistent with the scenario in which the bulges in more massive spirals formed
earlier than those in less massive spirals.
