Suppression of local heat flux in a turbulent magnetized intracluster medium

X-ray observations of hot gas in galaxy clusters often show steeper temperature gradients across cold fronts - contact discontinuities, driven by the differential gas motions. These sharp (a few kpc wide) surface brightness/temperature discontinuities would be quickly smeared out by the electron thermal conduction in unmagnetized plasma, suggesting significant suppression of the heat flow across the discontinuities. In fact, the character of the gas flow near cold fronts is favourable for suppression of conduction by aligning magnetic field lines along the discontinuities. We argue that a similar mechanism is operating in the bulk of the gas. Generic 3D random isotropic and incompressible motions increase the temperature gradients (in some places) and at the same time suppress the local conduction by aligning the magnetic field lines perpendicular to the local temperature gradient. We show that the suppression of the effective conductivity in the bulk of the gas can be linked to the increase of the frozen magnetic field energy density. On average the rate of decay of the temperature fluctuations d <>/dt decreases as << B-2 >>(-1/5).