How does temperature affect dynamic equilibrium?

Temperature affects to the opposite side that is appears in the equation. Take this equilibrium reaction for example:

A + B <-> C + D + heat

In this equation heat is on the product side, therefore heat is a product of the reaction. Depending on what you do with the temperature will affect the equilibrium. If you are going to increase the temperature you are going to force the reaction to proceed in reverse. If you lower the temperature you will for the reaction to precede forward. This is due to Le Chatelier's Principal. Le Chatelier said that if there is a stress applied to a system (or chemical equation) the system will move in such a way to elevate the stress.

In this case the stress is the temperature. If you lower the temperature the system will want to create more to replace the heat that is being lost, so the reaction proceeds forwards. If temperature is increased the reaction will want to remove the excess heat and proceed backwards (or reverse) to remove it.