The circular DNA is likely to have higher Tm than the linear one. You can actually do a quick analysis using a SYBR green dye based melt-profile analysis on a real-time PCR instruments. Take both the samples (a circular plasmid and a linearized one) purify and redissove in same buffer conditions and do a melt-profiling analysis....
Well this is an old question and was looked at specifically a long time ago (see J.Vinograd et al. J. Mol.Biol.33:173-197 (1968) "Early and late helix-coil transitions in closed circular DNA". They showed through heat denaturation that there is a little bit of early melting in the closed circular form compared to the open circular form (which is nicked and behaves like linear DNA), but the large majority of the melting (as measured by changes in optical density) happens at higher temperatures than for the open circular form, although it happens less cooperatively (fig 6 ). There are several other publications roughly confirming this outcome. As Malcolm noted the ccc form will snap back as long a it doesn't get nicked.