List<Messaging.SingleEmailMessage> messages = new List<Messaging.SingleEmailMessage>();
Messaging.SingleEmailMessage theMessage = new Messaging.SingleEmailMessage();
theMessage.setTemplateId(emailTemplateId);
theMessage.setTargetObjectId(this.myCase.ContactId);
List<String> toAddress = new List<String>();
toAddress.add(this.myCase.Contact.Email);
theMessage.setToAddresses(toAddress);
theMessage.setWhatId(this.myCase.Id);
theMessage.setSaveAsActivity(true); // Only saves to TargetObjectId
messages.add(theMessage);
Messaging.SendEmailResult[] results = Messaging.sendEmail(messages);

EmailTemplate ET = new EmailTempalte([Select id,Body, HtmlValue,Subject FROM EmailTemplate Where Id =: emailTemplateId]);

EmailMessage em = new EmailMessage();
               em.subject = ET.subject;
               em.body = ET.body;
               em.HtmlBody = ET.htmlValue;
               em.ParentId = case.id;
               insert em;