  If the tensor-to-scalar ratio $r$ of cosmological perturbations takes a large
value $r\sim 0.1$, which may be inferred by recent BICEP2 result, we can hope
to determine thermal history, in particular, the reheating temperature, $T_R$,
after inflation by space-based laser interferometers. It is shown that upgraded
and upshifted versions of DECIGO may be able to determine $T_R$ if it lies in
the range $6\times 10^6< T_R < 5\times 10^7$GeV and $3\times 10^7<T_R<2\times
10^8$GeV, respectively. Although these ranges include predictions of some
currently plausible inflation models, since each specification can probe $T_R$
of at most a decade range, we should determine the specifications of DECIGO
with full account of constraints on inflation models to be obtained by
near-future observations of temperature anisotropy and B-model polarization of
the cosmic microwave background radiation.
