We report on a search for double beta decay of $^{130}$Te to the first $0^{+}$ excited state of $^{130}$Xe using a 9.8 kg$cdot$yr exposure of $^{130}$Te collected with the CUORE-0 experiment. In this work we exploit different topologies of coincident events to search for both the neutrinoless and two-neutrino double-decay modes. We find no evidence for either mode and place lower bounds on the half-lives: $tau^{0 u}_{0^+}>7.9cdot 10^{23}$ yr and $tau^{2 u}_{0^+}>2.4cdot 10^{23}$ yr. Combining our results with those obtained by the CUORICINO experiment, we achieve the most stringent constraints available for these processes: $tau^{0 u}_{0^+}>1.4cdot 10^{24}$ yr and $tau^{2 u}_{0^+}>2.5cdot 10^{23}$ yr.
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