The AC is outside of security and has showers and is open during the hours that you are there. That is the best of the Oneworld lounges and probably the only one that you would have access to at FRA. It is upstairs above the AA ticket counters (across from the walkway to the Sheraton hotel). If you don't have Oneworld status, you cannot access any lounge based on arriving in CX J. The hotel does sell day rooms (but expensive, it would be over USD 100 for a few hours).