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Of course, temperature increase generally increases the rate of most chemical reactions, however, for a typical $S_N1$ reaction, we may invoke the following elemental step:

$RCH(X)R'rightleftharpoonsRC^+HR' +X^-$

And this is the rate determining step of the reaction.........

And because this, the rate determining step, involves BOND-BREAKING, we would predict that an increase in temperature should result in the production of more $RC^+HR$ species, and thus an INCREASE in the rate of reaction..........

Another way to look at this is to include heat, i.e. $Delta$, as a virtual reactant.............

$RCH(X)R' +DeltarightleftharpoonsRC^+HR' +X^-$

If we raise the temperature, we supply $Delta$, and, therefore, we should drive the equilibrium to the RIGHT as shown.

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