Please find here a sample reinstatement letter - http://www.mnsu.edu/iso/forms/Reinstatement%20letter%20template.doc
here is another sample with additional information that may be helpful - http://em.csuchico.edu/aap/Undergrad/forms/appeal.pdf
You do not need any additional "cover" letter.
Please be sure to attach copies of required documents.
Let me know if you need clarification.