There is no specific kind of communication that can be used to reduce emotion in such a situation. Any type of communication (phone call, letter, etc) is as likely to increase emotion as to reduce it. What is vital is the content and tone of the communication.
Ideally, the communication can reduce emotion by giving the customer at least some of what they want. If this is not possible, the only chance to reduce emotion is to be conciliatory. In face to face or phone interactions, the representative of the firm must repeatedly apologize and must not make any aggressive statements that serve to make the customer even angrier. This may not work since the bottom line is that the customer is not getting what they want, but it is the only real hope for reducing emotion in such a situation.
This is a very difficult, but very necessary thing for customer service agents to do. Many customers who contact customer service are unhappy about something and it is important to defuse their anger in order to keep them as customers. This can be accomplished by skillful communication, but it is not always possible.
In order to reduce emotion, customer service agents must be understanding and sympathetic. There is nothing worse than an agent who treats a customer's concerns in a brusque manner -- brushing off their concerns as if they were not valid.
An agent must, instead, be able to communicate true sympathy. They must not sound like they are reading off a sheet. Ideally, they would also be able to fix the customer's problem in some way. If, however, there is nothing that can be done about the customer's problem, they must sound like they truly feel badly about it. This is the only possible way to reduce the emotion on the part of the customer.