Dynamics of accretion discs of young stars with a fossil large-scale magnetic field is investigated. The presented magneto-gas-dynamic (MHD) model of accretion discs includes the equations of Shakura and Sunyaev, induction equation, equations of thermal and collisional ionization. The induction equation takes into account Ohmic and magnetic ambipolar diffusion, magnetic buoyancy. The influence of Ohmic and ambipolar heating on the thermal structure of accretion discs is considered, and the influence of the considered dissipative MHD effects on the temperature of the accretion discs around the classical T Tauri star is analyzed. Simulations show that Ohmic and ambipolar heating operates near the borders of the region with a low ionization fraction ('dead' zone). The temperature grows by ~ 1000K near the inner boundary of the 'dead' zone, r ≈ (0.5 - 1)AU, and by ~ 100K near its outer boundary, r ≈ (30 - 50)AU.