  Gibbs fields with continuous spins are studied, the underlying graphs of
which can be of unbounded vertex degree and the spin-spin pair interaction
potentials are random and unbounded. A high-temperature uniqueness of such
fields is proved to hold under the following conditions: (a) the vertex degree
is of tempered growth, i.e., controlled in a certain way; (b) the interaction
potentials $W_{xy}$ are such that $\|W_{xy}\|=\sup_{\sigma,\sigma'}
|W_{xy}(\sigma, \sigma')|$ are independent (for different edges $\langle x, y
\rangle$), identically distributed and exponentially integrable random
variables.
