  The N-dimensional radial Schr\"odinger equation has been solved using the
analytical exact iteration method (AEIM), in which the Cornell potential is
generalized to finite temperature and chemical potential. The energy
eigenvalues have been calculated in the N-dimensional space for any state (n,
l). The present results have been applied for studying quarkonium properties
such as charmonium and bottomonium masses. The binding energies and the mass
spectra of heavy quarkonia are studied in the N-dimensional space. The
dissociation temperatures for different states of heavy quarkonia are
calculated in the three dimensional space. The influence of dimensionality
number (N) has been discussed on the dissociation temperatures. A comparison is
studied with other recent works. We conclude that the AEIM successes to predict
the heavy-quarkonium properties at finite temperature and chemical potential.
