Anomalous transport caused by fluctuations of resistive pressure‐driven modes is discussed within the framework of magnetohydrodynamics (MHD). The nonlinear‐reduced equations describing fluctuations localized near a particular magnetic field line are derived for tokamak and reversed‐field‐pinch (RFP) plasmas, taking into account nonzero viscosity and heat conductivity. For an ideally stable but resistively slightly unstable plasma, the anomalous transport is caused particularly by convective motions. The convection is studied as bifurcation from the linearly unstable equilibrium and the expression of the anomalous transport in a tokamak plasma is obtained as a function of the mean pressure gradient near the critical point. In order to evaluate the effects of the convection on the anomalous transport under various conditions, the reduced equations are also solved numerically. It is found that Nusselt number, that is, the ratio of the total heat conductivity including the anomalous heat transport to the classical collisional heat conductivity, is significantly large under some conditions. This partially accounts for the large heat losses in controlled thermonuclear fusion devices.