  In the perspective of the outstanding developments of high-precision
measurements of fundamental constants using polar molecules related to ultimate
checks of fundamental theories, we investigate the possibly counterproductive
role of black-body radiation on a series of diatomic molecules which would be
trapped and observed for long durations. We show that the absorption of
black-body radiation at room temperature may indeed limit the lifetime of
trapped molecules prepared in a well-defined quantum state. Several examples
are treated, corresponding to pure rotational absorption, pure vibrational
absorption or both. We also investigate the role of a black-body
radiation-induced energy shift on molecular levels and how it could affect
high-precision frequency measurements.
