  The physical properties, evolution, and fragmentation of massive dense cores
(MDCs, $\sim$ 0.1 pc) are fundamental pieces in our understanding of high-mass
star formation. We aim to characterize the temperature, velocity dispersion,
and fragmentation of the MDCs in the Cygnus X giant molecular cloud and to
investigate the stability and dynamics of these cores. We present the Karl G.
Jansky Very Large Array (VLA) observations of the NH$_3$ (J,K) = (1,1) and
(2,2) inversion lines towards 35 MDCs in Cygnus X, from which we calculated the
temperature and velocity dispersion. We extracted 202 fragments ($\sim$ 0.02
pc) from the NH$_3$ (1,1) moment-0 maps with the GAUSSCLUMPS algorithm. We
analyzed the stability of the MDCs and their NH$_3$ fragments through
evaluating the corresponding kinetic, gravitational potential, and magnetic
energies and the virial parameters. The MDCs in Cygnus X have a typical mean
kinetic temperature T$_K$ of $\sim$ 20 K. Our virial analysis shows that many
MDCs are in subvirialized states, indicating that the kinetic energy is
insufficient to support these MDCs against their gravity. The calculated
nonthermal velocity dispersions of most MDCs are at transonic to mildly
supersonic levels, and the bulk motions make only a minor contribution to the
velocity dispersion. Regarding the NH$_3$ fragments, with T$_K$ $\sim$ 19 K,
their nonthermal velocity dispersions are mostly trans-sonic to subsonic.
Unless there is a strong magnetic field, most NH$_3$ fragments are probably not
in virialized states. We also find that most of the NH$_3$ fragments are
dynamically quiescent, while only a few are active due to star formation
activity.
