  Whispering gallery resonators (WGR's), based on total internal reflection,
possess high quality factors in a broad spectral range. Thus, nonlinear optical
processes in such cavities are ideally suited for the generation of broadband
or tunable electromagnetic radiation. Experimentally and theoretically, we
investigate the tunability of optical parametric oscillation in a radially
structured WGR made of lithium niobate. With a 1.04 /mum pump wave, the signal
and idler waves are tuned from 1.78 to 2.5 \mum - including the point of
degeneracy - by varying the temperature between 20 and 62 {\deg}C. A weak
off-centering of the radial domain structure extends considerably the tuning
capabilities. The oscillation threshold lies in the mW-power range.
