A cover letter is probably written before you've seen the workplace from the inside. The thank you note is more personal and lets you talk about the workplace you have seen, and how you feel you would fit into that workplace. One way to do this is to describe things you've done that are like the job you seek. If you want an office job, write about records you have kept. If you got a chance to see the work station, describe yourself at that workstation.
People make decisions based on things they can imagine as possible.
Put that picture in the employer's head, and you can help the employer decide in your favor. For instance, if the employer emphasized working with details, explain how detailed work is one of your strengths. If your prospective employer is interested in government or politics, you might mention your ongoing interest in civic affairs.