A search was conducted for the 2\(^+_2\) excitation of the 7.65 MeV, 0\(^+_2\), Hoyle state in \(^{12}\)C using the \(^{12}\)C(\(^{12}\)C, \(^{12}\)C[3α]) \(^{12}\)C reaction. The analysis focussed primarily on the 9.7 MeV region in the \(^{12}\)C excitation energy spectrum and no evidence of a resonance was found. Monte Carlo simulations were used to investigate the minimum strength at which a resonance would need to exist in order to be resolved by the experimental setup used. The possibility was also investigated that the 2\(^+_2\) resonance may be observed in the \(^{12}\)C(\(^{12}\)C, \(^{12}\)C[\(^8\)Be*+α]) \(^{12}\)C reaction channel, though the methods contained within this thesis allowed only limited analysis of reaction channels involving non-zero spin states in the intermediate \(^8\)Be nucleus; no evidence of a resonance was found. Further analysis of the 9.6 MeV and 10 MeV regions of the \(^{12}\)C excitation energy spectrum also revealed no clear sign of a 2\(^+_2\) resonance.