  Exploiting two interfering fields which are initially in the same temporal
mode but with the spectra altered by propagating through different fibers, we
characterize how the spectra of temporal modes changes with the fiber induced
dispersion by measuring the fourth-order interference when the order number and
bandwidth of temporal modes are varied. The experiment is done by launching a
pulsed field in different temporal modes into an unbalanced Mach-Zehnder
interferometer, in which the fiber lengths in two arms are different. The
results show that the mode mismatch of two interfering fields, reflected by the
visibility and pattern of interference, is not only dependent upon the amount
of unbalanced dispersion but also related to the order number of temporal mode.
In particular, the two interfering fields may become orthogonal under a modest
amount of unbalanced dispersion when the mode number of the fields is $k\geq2$.
Moreover, we discuss how to recover the spectrally distorted temporal mode by
measuring and compensating the transmission induced dispersion. Our
investigation paves the way for further investigating the distribution of
temporally multiplexed quantum states in fiber network.
