We have shown that there exists low-frequency growing modes driven by a global temperature gradient in electron and ion plasmas, by linear perturbation analysis within the frame work of plasma Kinetic theory. The driving force of the instability is the local deviation of the distribution function from the Maxwell-Boltzmann due to global temperature gradient. Application to the intracluster medium shows that scattering of the particles due to waves excited by the instability is possible to

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... mean free paths of electron and ion down to five to seven order of magnitude than the mean free paths due to Coulomb collisions. This may provide a hint to explain why hot and cool gas can co-exist in the intracluster medium in spite of the very short evaporation time scale due to thermal conduction if the conductivity is the classical Spitzer value. Our results suggest that the realization of the global thermal equilibrium is postponed by the local instability which is induced for quicker realization of local thermal equilibrium state in plasmas. The instability provides a new possibility to create and grow cosmic magnetic fields without any seed magnetic field.