JD Edwards E1 is not on the vulnerable list for the Heartbleed bug
Oracle has recently published a list of the software that could be vulnerable to the Heartbleed bug, and JD Edwards EntepriseOne has been listed as not vulnerable.
This only refers to the E1 software and it is not extensible to any third party products used with E1.
Link:
http://www.oracle.com/technetwork/topics/security/opensslheartbleedcve-2014-0160-2188454.html
Note:
Oracle Linux 6 has been identified as likely vulnerable and there is already a fix:
Oracle Linux 6 [Product ID 1309] MOS https://support.oracle.com/rs?type=doc&id=1663998.1