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 alpha particle heating, the time variation of the plasma parameters causes a change in the alpha heating power. This provides a new picture of the thermal instability in burning plasmas