Setting socket timeouts breaks handshake

I'm seeing a weird issue when starting a TLS connection to any host. If I don't set any timeout on the socket, it works fine. If I do, it breaks before the handshake with a OpenSSL.SSL.WantReadError. For example if I set timeout to 100, it will break after a second anyway.

For now I use a workaround of setting a timeout on connection, but then removing it before the handshake.

s = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
s.settimeout(2)

ctx = OpenSSL.SSL.Context(OpenSSL.SSL.TLSv1_METHOD)
ctx.set_options(OpenSSL.SSL.OP_NO_SSLv2 | OpenSSL.SSL.OP_NO_SSLv3)
ctx.set_verify(OpenSSL.SSL.VERIFY_NONE, lambda _a, _b, _c, _d, _e: None)
conn = OpenSSL.SSL.Connection(ctx, s)
conn.set_tlsext_host_name(hostname.encode('utf-8'))
conn.connect((ip, port))

# s.settimeout(None)  # the workaround

try:
    conn.do_handshake()
except OpenSSL.SSL.WantReadError:
    # this happens on every connection

I'm running on Python 3.4.1, OpenSSL 0.14.

Start with the socket-timeout reproducer in the issue and inspect OpenSSL.SSL.Connection.connect() and do_handshake() behavior when the underlying socket has a timeout. Compare it with the documented workaround that removes the timeout before the handshake. Done means a TLS handshake succeeds without requiring that workaround while preserving timeout behavior.