Anisotropic thermal conduction plays an important role in various astrophysical systems. One of the most stringent tests of thermal conduction can be found in supernova remnants. In this paper we study anisotropic thermal conduction and examine the physical nature of the flux of thermal conduction in the classical and saturated limits. We also present a temporally second-order accurate implicit-explicit scheme for the time-update of thermal conduction terms within a numerical MHD scheme. Several simulations of supernova remnants are presented for a range of ISM parameters. The role of thermal conduction in such remnants has been studied. We find that thermal conduction produces cooler temperatures and higher densities in the hot gas bubbles that form in the remnants. The effect of thermal conduction in changing the thermal characteristics of the hot gas bubble increases as the remnant propagates through denser ISMs. Remnants evolving in denser ISMs are shown to make a faster transition to a centre-bright x-ray morphology, with the trend emerging earlier in hard x-rays than in the soft x-rays.
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