  Kaon in-medium masses and mean-field potentials are calculated in
isotopically symmetric pion matter to one loop of chiral perturbation theory.
The results are extended to RHIC temperatures using experimental data on $\pi
K$ scattering phase shifts. The kaon in-medium broadening results in an
acceleration of the $\phi \to K\bar{K}$ decay. The increased apparent dilepton
branching of the $\phi $-mesons, observed recently by NA50, NA49, and the
PHENIX collaborations at RHIC, is interpreted in terms of rescattering of
secondary kaons inside of the pion matter.
