What is the procedure for removing a temporary filling? will the dentist inject the patient?

It depends: On a few variables including the status of the dental pulp, the material used for the temp filling, and the preference of the patient. I'd say about half the time, an injection is unnecessary in my world and the other half absolutely requires it. Sometimes fear of anticipated pain rules the day and an injection is placed when it may not have really been needed. Every situation is unique.

Temporary fillings: Are removed with a hi speed handpiece with a local anesthetic is the tooth is not root canaled. If the tooth is root canaled the dentist may numb the gum tissue or not depending on the size of the build up needed.

Normally yes: A temporary filling is often in a tooth because it might had been very deep and close to the nerve when it was placed (as a precaution.) to remove it, some drilling has to be done, and the sensitivity may not be comfortable (unless the nerve is already removed from the tooth with a root canal.).