Below there is the source of the sun.net.www.protocol.http.HttpURLConnection.setRequestProperty() method:

    public void setRequestProperty(String key, String value) {
        if (connected)
            throw new IllegalAccessError("Already connected");
/* There should be only one header per key, but special-case
* HTTP cookies.
*/
if ("set-cookie".equalsIgnoreCase(key)) {
requests.add(key, value);
} else {
requests.set(key, value);
}
    }

But the field in the request to server is called "cookie".
[Victor Lapitsky, SPb HotJava Team, ###@###.###