A new three-dimensional numerical simulation of turbulent transport phenomena in an open system controlled by an external heat source and a sink is proposed by virtue of self-consistent calculation of the multi-scale interactions. External heating is applied to an equilibrium including micro-turbulence, and thermal transport due to the turbulence is investigated for a case including small-scale magnetic fluctuation and for a case including not only small-scale but also large-scale magnetic fluctuation by numerically solving a reduced set of two-fluid equations. In the first case turbulent transport controlled by external heating is calculated and profile stiffness in electromagnetic turbulence is examined. In the second case a change in turbulent transport in the presence of a tearing mode, which is large-scale magnetic fluctuation, is examined. In this case multi-scale interactions between micro-turbulence and the tearing mode play the key role in thermal transport. When the tearing mode appears in a quasi-equilibrium including micro-turbulence and zonal flow, the energy spectrum of micro-turbulence is changed so that the energy of the dominant toroidal mode representing micro-turbulence is reduced and the energy of the small toroidal mode increases. At the same time the gradient of ion temperature is reduced and the heat flux increases around the magnetic islands due to the tearing mode.