We investigate the thermal history in the universe with a variable cosmological term. In particular, we show how the formation of important molecules such as H2 and HD is influenced during the epoch for the redshift from 10000 to 1. These molecules should dominate the cooling process of primordial gas clouds which triggers the collapse of them. It is found that the molecular formation is quickened by Δz ∼ 1000 compared with the case in the standard model due to the variable cosmological term. The qualitative estimate of the mass of the first objects has been performed with use of the time scales related to the thermal evolution. It is suggested that the formation scenarios of the first objects studied so far could be changed drastically if the variable cosmological term is included in the thermal history in the universe.
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