why higher temp favour energetically controlled path while lower temp favour kinetically control path?

Answer 1

A high temperature will only favour those reactions which are endothermic. To be spontaneous, endothermic reactions require there to be an increase in entropy. You can understand this from the Gibbs Free Energy equation deltaG = deltaH - TdeltaS. deltaG will tend to become negative as T increases.
However, all reactions proceed faster with an increase in temperature, since a greater proportion of molecules have the minimum energy required to react - the activation energy.
A low temperature will favour exothermic reactions, and will slow down all reactions.

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