With every letter it is important to identify what is the aim of your writing. There are many types of writing used in letters but in the circumstance of writing to someone you do not know, it is most common for the purpose of the interaction to be a PERSUASION (to change the reader from one opinion to another), an ARGUMENT (to put forward an opinion for a subject) or to INFORM (to tell the person of some information).
The flow and general direction of the letter will be determined by the purpose of the letter. However, the main point of this writing is the TONE and AUDIENCE. It should be clear that when writing in this situation you should always be formal in your writing. This can be achieved by some simple, subtle changes to your style and vocabulary. For example: writing 'Dear Sir/Madam,' as a salutation instead of 'Hi/Hello', 'I am writing to you today...' oppose to writing 'I wanted to write to you because...' and to end the letter 'Yours faithfully'. A rule of thumb is to always keep in mind that this person should be regarded in a polite, respectful and dignified manner and that must be reflected in your writing.