Before we answer this question, we must know the reason for using a torque wrench.  

The purpose of a torque wrench is to provide consistent torque, accurately.    

This accuracy is calibrated based on the length of the torque wrench.

Adding an extension shall affect the length of the Torque Wench itself thus affecting the torque applied to the fastener. The accuracy of the torque wrench is typically specified by the manufacturer as per a certain range of length of wrenches. When an extension is used the additional leverage can increase the torque applied or decrease it depending on the shape and size of the extension.

The torque must be set accordingly to compensate for the added leverage. Torque Wrench manufacturers can guide you according to the adjustment to be made as per the extension.

The accuracy of a Torque wrench with an extension can be affected by the following factors as well:

• Wear and tear
• Temperature
• Calibration Frequency or lack thereof

Torque can be affected by the following factors apart from the ones mentioned above:

• Extension between a socket and the torque wrench
• Orientation of the adaptor to the torque wrench

The formula to adjust your torque wrench setting is:

Setting = (torque wrench length x torque desired) ÷ (torque wrench length + adapter extension length)

Regular calibration and maintenance are essential to ensure the continued accuracy of a torque wrench, regardless of whether extensions are used or not.

There could be safety hazards especially while using higher-powered Hydraulic Torque Wrenches and Electrical Torque wrenches.

Correct dimensional measurements of the Bolt or stud and Nut with the knowledge of the conditions of the flange they are holding. 

Other accessories such as Torque Multipliers, Back-Up Wrenches, Slugging wrenches and Lubrication and surrounding conditions are also to be considered before torqueing operations can begin.

In Conclusion, It is evident that several factors affect the amount of torque a bolt needs so that it can be sufficiently tightened, also the tool that is used to tighten said bolt is also affected by factors such as extensions and modifications to its length.