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We study the dissipative thermodynamics of vortex lines in layered superconductors within a simple string model in the dilute limit of negligible vortex interactions and compute the specific heat C-upsilon in the presence of arbitrary dissipation. The interplay of dissipation, inertia, and elasticity is shown to control the qualitative thermodynamical behavior and their relative amount determines two very distinct regimes for the specific heat. In the dissipation-dominated case we find a behavior C-upsilon similar to root T for a large interval of temperature below T-c.