  We consider the decay of a massive particle under the complete or partial
domination of the kinetic energy density generated by a quintessential
exponential model and we impose a number of observational constraints
originating from nucleosynthesis, the present acceleration of the universe and
the dark-energy-density parameter. We show that the presence of kination causes
a prolonged period during which the temperature is frozen to a plateau value,
much lower than the maximal temperature achieved during the process of
reheating in the absence of kination. The decoupling of a cold dark matter
particle during this period is analyzed, its relic density is calculated both
numerically and semi-analytically and the results are compared with each other.
Using plausible values (from the viewpoint of particle models) for the mass and
the thermal averaged cross section times the velocity of the cold relic, we
investigate scenaria of equilibrium or non-equilibrium production. In both
cases, acceptable results for the cold dark matter abundance can be obtained,
by constraining the initial energy density of the decaying particle, its decay
width, its mass and the averaged number of the produced cold relics. The
required plateau value of the temperature is, in most cases, lower than about
40 GeV
