  We present a potential of which the short-distance part is given by one gluon
exchange plus perturbative one- and two-loop corrections and of which the
large-distance part exhibits a temperature-dependent constant value. The
Schrodinger equation with this temperature-dependent potential yields a
temperature dependence of the mesonic quark-antiquark relative-motion wave
function and of meson masses. The temperature dependence of the potential, the
wave function and the meson masses brings about temperature dependence of cross
sections for the nonresonant reactions pi pi -> rho rho for I=2, KK -> K* K*
for I=1, KK* -> K* K* for I=1, pi K -> rho K* for I=3/2, pi K* -> rho K* for
I=3/2, rho K -> rho K* for I=3/2 and pi K* -> rho K for I=3/2. As the
temperature increases, the rise or fall of peak cross sections is determined by
the increased radii of initial mesons, the loosened bound states of final
mesons, and the total-mass difference of the initial and final mesons. The
temperature-dependent cross sections and meson masses are parametrized.
