  It is shown that space-based gravitational wave detectors such as DECIGO
and/or Big Bang Observer (BBO) will provide us with invaluable information on
the cosmic thermal history after inflation and they will be able to determine
the reheat temperature $T_R$ provided that it lies in the range preferred by
the cosmological gravitino problem, $T_R\sim 10^{5-9}$ GeV. Therefore it is
strongly desired that they will be put into practice as soon as possible.
