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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., Comment: 4 pages, 5 figures