Why does material resistance increase with temperature but electrolyte internal resistance decrease with increase in temperature? The question is pretty much in the title itself, why does the internal resistance decrease with the increase in the temperature of electrolyte? Is it related to the electrolyte bring a fluid or something? 
 A: It's because the mechanism of conduction in a metal is different to the conduction in an electrolyte.
In a metal the electrons are almost free, and resistance is due to electrons scattering off defects and lattice vibrations. Increasing the temperature increases the amplitude of the lattice vibrations and therefore increases the scattering.
In an electrolyte current is carried by moving ions, e.g. (hydrated) Na$^+$ and Cl$^-$ in saline, and the resistance is due to the limited mobility of these ions. Since the ion mobility increases with temperature the resistance of electrolytes generally falls with increasing temperature.
I must admit it had never occurred to me that because of this the internal resistance of a battery would fall with temperature, but assuming the internal resistance is due to the resistance of the electrolyte in batteries it makes sense. For batteries with liquid electrolytes, like lead-acid batteries, the reason is obvious but even for batteries using semisolid electrolytes the ion mobility is likely to rise with increasing temperature.
