We investigated temperature dependent Raman spectra of the one-dimensional spin-ladder compound SrCu2O3. At low temperatures a two-magnon peak is identified at 3160+/-10 cm^(-1) and its temperature dependence analyzed in terms of a thermal expansion model. We find that the two-magnon peak position must include a cyclic ring exchange of J_cycl/J_perp=0.09-0.25 with a coupling constant along the rungs of J_perp approx. 1215 cm^(-1) (1750 K) in order to be consistent with other experiments and theoretical results.