  We show that a mini-thermal inflation occurs naturally in a class of gauge
mediation models of supersymmetry (SUSY) breaking, provided that the reheating
temperature T_R of the primary inflation is much higher than the SUSY-breaking
scale, say T_R > 10^{10} GeV. The reheating process of the thermal inflation
produces an amount of entropy, which dilutes the number density of relic
gravitinos. This dilution renders the gravitino to be the dark matter in the
present universe. The abundance of the gravitinos is independent of the
reheating temperature T_R, once the gravtinos are thermally produced after the
reheating of the primary inflation. We find that the thermal leptogenesis takes
place at T_L\simeq 10^{12-14} GeV for m_{3/2}\simeq 100 keV - 10 MeV without
any gravitino problem.
