The anomalous transport and turbulence driven by a combination of the toroidal ion temperature gradient (ITG) mode and dissipative trapped electron (DTE) mode are studied for a plasma in the dissipative regime. The results from numerical mode coupling simulations show a good agreement with the results from quasilinear theory. A transition from the neo-Alcator scaling of the energy confinement time with density to a saturated state is obtained. It is shown that ion heat pinch effects (inward transport) may exist in the process of thermodynamic relaxation of the system.