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In protoplanetary disks, the inner boundary between the turbulent and laminar regions is a promising site for planet formation because solids may become trapped at the interface itself or in vortices generated by the Rossby wave instability. The disk thermodynamics and the turbulent dynamics at that location are entwined because of the importance of turbulent dissipation on thermal ionization and, conversely, of thermal ionisation on the turbulence. However, most previous work has neglected this dynamical coupling and have thus missed a key element of the physics in this region. In this paper, we aim to determine how the the interplay between ionization and turbulence impacts on the formation and evolution of vortices at the interface between the active and the dead zones. Using the Godunov code RAMSES, we have performed a 3D magnetohydrodynamic global numerical simulation of a cylindrical model of an MRI--turbulent protoplanetary disk, including thermodynamical effects as well as a temperature-dependant resistivity. The comparison with an analogous 2D viscous simulation has been extensively used to help identify the relevant physical processes and the disk's long-term evolution. We find that a vortex formed at the interface, due to Rossby wave instability, migrates inward and penetrates the active zone where it is destroyed by turbulent motions. Subsequently, a new vortex emerges a few tens of orbits later at the interface, and the new vortex migrates inward too. The sequence repeats itself, resulting in cycles of vortex formation, migration, and disruption. This behavior is successfully reproduced using two different codes. In this paper, we characterize this vortex life cycle and discuss its implications for planet formation at the dead/active interface. Our simulations highlight the importance of thermodynamical processes for the vortex evolution at the dead zone inner edge., Comment: 13 pages, 15 figures