  The in-medium mass and decay width of the $\phi$ meson in the hot asymmetric
strange hadronic matter are calculated using an effective Lagrangian approach
for $\phi$ $K\bar K$ interaction. The in-medium contributions of $K \bar K$
loop to the $\phi$ meson self-energy are computed by the medium modified kaon
and antikaon mass which is evaluated using the chiral SU(3) model. To deal with
the ultraviolet divergence, we regularize the loop integral of self-energy with
a dipole form factor, and present the results for cut-off mass, $\Lambda_c$=3
GeV. In chiral model calculations, for strange matter, we find that the mass of
kaons and antikaons decreases with the increase in baryonic density whereas the
finite temperature causes an increase in the mass. We observed that the
in-medium $\phi$ meson mass decreases slowly with baryonic density whereas the
decay width increases rapidly. The results in the present investigation support
result in the literature which indicate a small downward shift in mass and a
large broadening in the decay width. In the asymmetric strange hadronic matter,
the study of the $\phi$ mesons can be relevant for the compressed strange
baryonic matter and experimental observables such as dilepton spectra which can
result from the experiments in the future FAIR facility at GSI.
