You can alternately set a custom header using the MimeMessage.addHeader(String, String) method, and insert the formatted date using SimpleDateFormat.format(Date):
String dateFormat = "yyyy-MM-dd HH:mm:ss"; // you specify the format for your date
String formattedDate = new SimpleDateFormat(dateFormat).format(new Date());
MimeMessage mimeMessage = //get message from wherever
mimeMessage.addHeader("Date", formattedDate);