After a whole day of R&D, here's how:
URL url = new URL(urlAddress);
HttpURLConnection connection = (HttpURLConnection) url.openConnection();
connection.setDoInput(true);
connection.connect();
InputStream input = connection.getInputStream();
Bitmap immutableBpm = BitmapFactory.decodeStream(input);
Bitmap mutableBitmap = immutableBpm.copy(Bitmap.Config.ARGB_8888, true);
View view = new View(this);
view.draw(new Canvas(mutableBitmap));
String path = Images.Media.insertImage(getContentResolver(), mutableBitmap, "Nur", null);
Uri uri = Uri.parse(path);
final Intent emailIntent = new Intent(android.content.Intent.ACTION_SEND);
emailIntent.putExtra(Intent.EXTRA_STREAM, uri);
emailIntent.setType("image/png");
startActivity(Intent.createChooser(emailIntent, "Send mail..."));
Hope this snippet helps you with attaching an image from a URL to an email intent in Android! :)