Why is exothermic reactions are favoured by low temperature while endothermic reactions are favoured by high temperature?
I'll try and simplify the answer.
Looking at the image above, imagine the products sitting above the letter D and the reactants sitting below the letter B. Now, imagine the particles involved in the reaction moving since they have kinetic energy. It is much easier for the reactants to climb up the top of the hill labeled C then it is for the products to climb up the hill. Once a reactant climbs the hill and slides down to products it will not be able to go back to reactants by climbing up the hill unless we give them more energy by raising temperature. Raising temperature allows the products to climb up the hill and go to reactants.
The forward reaction in the diagram is exothermic and the reverse is endothermic. So, the exo is favored at low T and the endo at high T.
You can also look at the equation delta G = delta H - Tdelta S.
Make up some numbers for delta H and delta S. You will see that endo reactions becomes more spontaneous as you raise T and exo reactions become more spontaneous as you lower T regardless of delta S.
You have to know that when you have a chemical equilibrium that is subjected to a change in concentration, temperature or pressure,then this equilibrium will readjust itself to counteract the effect of the applied change and a new equilibrium is established.
So, if the reaction is exothermic. This means it produces heat. So, if we decrease the temperature (low temperatures), the equilibrium will tend to counteract this effect and favor the reaction that produces heat to increase the temperaure of the system.
On the other hand, if the reaction is endothermic. This means it consumes heat. So, if we increase the temperature (high temperatures), the equilibrium will tend to counteract this effect and favor the reaction that consumes heat to decrease the temperaure of the system.
In sum, exothermic reactions are favoured by low temperature while endothermic reactions are favoured by high temperature