Some institutions require cover letter which is just like 'letter of intent' except that you have to mention your electives detail, sponsor's detail and details of the documents you have attached with your application.
You can view a sample cover letter below.

The Office of Undergraduate Medical Education
Medical Education Department
Henry Ford Hospital
Detroit, Michigan

SUBJECT : Electives application material

Dear XYZ,

I am currently a final year medical student at________________.
I plan to undertake my clinical electives at Henry Ford Hospital, as a visiting student, for a period of 4 weeks from April 3, 2010 to April 31, 2010 in the field of Cardiology . Dr. of Cardiology Dept. will be acting as my sponsor.
(Write something more like ‘letter of intent’)

Sincerely,

Name:
Address:
E-mail:
Cell Phone:
Home Phone:
Passport no:

SPONSORING FACULTY:
FACULTY DEPARTMENT: Department of Cardiology

I have sent the following documents, please check:

1. Completed International Student Elective Application.
2. Curriculum vitae
3. Official medical university transcript.
4. Letter of recommendation from the Dean.
5. Waiver for USMLE Step 1.
7. Letter of recommendations from Faculty of my own institute
6. Immunization record & Lab titre reports
7. Health insurance & Malpractice Insurance
8. Passport copy.