In a reaction, there is an exothermic and a endothermic side. Increasing the temperature will favour the endothermic side.
So if your reaction is exothermic, that means it must release heat if it shifts to the left. Then, since the left is exothermic, it shifts to the right (endothermic) to minimise this disturbance.
If your reaction is endothermic, that means it must absorb heat if it shits to the left. Then, since the left is endothermic, if you increase the temperature it shifts to the left (endothermic) to minimise this disturbance.
The above is much easier to understand if you think of 'heat' as a product or reactant. In an exothermic reaction, heat is on the product side of the equation. So if you increase this component, to minimise this disturbance you must shift the equilibrium to the LEFT to decrease the 'heat' amount - and vice versa.