This kind of stuff is done all the time. I had one system that ran a process which under worst-case conditions (once every week or so) could run for 10 hours.
I implemented it as a stand-alone application running as a
Java RMI server. The webapp on the front-end made remote calls to start/stop and monitor it. It didn't need a separate CPU to run on (the whole system, webserver and all usually peaked out at 13% CPU or less), but by isolating it, we were able to do things to the frontend server that would have been "held hostage" if we didn't want to interrupt the backend.
I'm suspecting that you're thinking of spinning up a secondary WebLogic server, but that's only one option and it's a fairly expensive one. You have lots of options. You can use web services to invoke the backed, JMS, MQ, or even RMI. You may find it useful to house the process in a generic container such as Apache Karaf or ServiceMix. Or you could do like I did and run as a stand-alone RMI server (although at the time, I had fewer choices).
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.