If the tensor-to-scalar ratio r of cosmological perturbations takes a large value r ∼ 0.1, which may be inferred from the recent BICEP2 result, we can hope to determine thermal history, in particular, the reheating temperature, TR, after inflation by space-based laser interferometers. It is shown that upgraded and upshifted versions of DECIGO may be able to determine TR if it lies in the range 6 × 106 < TR < 5 × 107 GeV and 3 × 107 < TR < 2 × 108 GeV, respectively. Although these ranges include predictions of some currently plausible inflation models, because each specification can probe TR of a range of at most a decade, we should determine the specifications of DECIGO taking full account of the constraints on inflation models to be obtained by near-future observations of temperature anisotropy and B-model polarization of the cosmic microwave background radiation.