Operating your wood stove at the correct temperature is a very important matter… if your stove is an older model with no glass door. If this type of wood stove burns too cold will create creosote buildup and pollution. Not to mention that if your wood-stove is burning too cold it is not really working efficiently. If the stove is burning too hot, this is 
not right as the it becomes a fire risk and could also accelerate corrosion within the metal flue, pipe, liner, and the wood stove itself. Using a flue pipe thermometer helps to remove the guesswork of determining the temperature of your wood stove.
If you own a more modern wood stove that does have a glass door, a flue pipe thermometer is not actually necessary. You can actually determine how hot the fire is simply by observing it. Also, there is no correct operating temperature for a wood stove as they are designed to release heat depending on the conditions. For example, in winter weather the temperature is higher than in the fall as the heating load is lower.
A normal reaction when using a wood burning stove is to see a constant fluctuating temperature. At the beginning of each new load of wood, the temperature will be high and depending on how you set the air control, this could lower and continually fall off until it is time for the next load of wood.
Resources: Avery’s, The Wood Heat Organization