A consistent numerical simulation is performed to study the dynamics in a steady state plasma with improved core confinement which is sustained by a bootstrap current and external drive. A new non-linear link between the profiles of the pressure, current and thermal conductivity is investigated. A self-organized oscillation (i.e. spatiotemporal limit cycle oscillation) of the plasma pressure and current, coupled by the variation of the confinement enhancement factor, is predicted to occur. In the presence of a particle heating, the time variation of the plasma parameters causes a change in the or heating power. This provides a new picture of the thermal instability in burning plasmas.