The method responseInputStream of HttpClientBase wraps an InputStream in order to close it when it is done reading. However, the wrapper only overwrites the single-byte read() method, every other method is delegated to its parent (java.io.InputStream). Therefore, the more efficient read-methods like read(byte b) are all implemented by reading one byte after the other.
In my test, it took 20 minutes to copy an index of 38 GB. With the provided small patch, this was reduced to less than 10 minutes.