You're going to need two things. You want your real-time thread to get priority, and preferably have it driven by a timer so you get (nearly) periodic measurements. Then, you're going to want a resource that can be used to communicate the values. That can either be a simple monitor, with a critical section so the timer thread can write into it, or it could be -- and very probably would be better as -- a FIFO, so that the GUI thread can eat up values whenever it has cycles.
In Java, the GUI (at least in Swing and similar) is already running a separate thread for UI interactions, so you're big issue is to set up your measurement thread. Have a look at Runnables.