Experimental kinetic energy release distributions obtained for the thermionic emission from C(n) (-) clusters, 10< or =n< or =20, exhibit significant non-Boltzmann variations. Using phase space theory, these different features are analyzed and interpreted as the consequence of contrasting shapes in the daughter clusters; linear and nonlinear isomers have clearly distinct signatures. These results provide a novel indirect structural probe for atomic clusters associated with their thermionic emission spectra.