  The ground states of Klein type spin models on the pyrochlore and
checkerboard lattice are spanned by the set of singlet dimer coverings, and
thus possess an extensive ground--state degeneracy. Among the many exotic
consequences is the presence of deconfined fractional excitations (spinons)
which propagate through the entire system. While a realistic electronic model
on the pyrochlore lattice is close to the Klein point, this point is in fact
inherently unstable because any perturbation $\epsilon$ restores spinon
confinement at $T = 0$. We demonstrate that deconfinement is recovered in the
finite--temperature region $\epsilon \ll T \ll J$, where the deconfined phase
can be characterized as a dilute Coulomb gas of thermally excited spinons. We
investigate the zero--temperature phase diagram away from the Klein point by
means of a variational approach based on the singlet dimer coverings of the
pyrochlore lattices and taking into account their non--orthogonality. We find
that in these systems, nearest neighbor exchange interactions do not lead to
Rokhsar-Kivelson type processes.
