Q:

Timer or other idea required to allow code to continue execution after calling method and JOptionPane

I need a way to allow my program to keep running code after this method is called.
Currently, it waits for half an hour, gets the info, stores it to the object WeatherCard, and displays it, and repeats.  But it hangs on the JOptionPane.  I need a way to make it so that the program either keeps going underneath the JOptionPane or to close the pane after about 10 seconds.  I am not sure how to work either into my code, currently
public void printWeatherCard(WeatherCard w, JFrame controlFrame) throws MalformedURLException, IOException{
    /* Displays a dialog box containing the temperature and location */
    BufferedImage img = ImageIO.read(new URL(w.imgSrc));
    ImageIcon icon = new ImageIcon(img);

    JOptionPane.showMessageDialog(controlFrame, "It is currently " + w.currentTemp + " \u00B0 F in " + w.location.city + ", " + w.location.state + ".\nCurrent humidity: " + w.currentHumidity + 
            "%.\nChance of precipitation: " + w.chancePrecip + "%.", "Weather Update: " + w.location.zipCode, JOptionPane.INFORMATION_MESSAGE, icon);
}

A:

Closing a modal dialog after some delay and updating the display behind a modal dialog are distinct issues.

In this example, a javax.swing.Timer is used to mark time, and the dialog is closed when a counter reaches zero or the user dismisses it.
A modal dialog only blocks user interaction. Add a modal dialog to this example to see that GUI updates continue in response to the javax.swing.Timer.
public void run() {
    ...
    f.setVisible(true);
    JOptionPane.showMessageDialog(dt, TITLE);
}

A:

But it hangs on the JOptionPane. I need a way to make it so that the
  program either keeps going underneath the JOptionPane or to close the
  pane after about 10 seconds. I am not sure how to work either into my
  code, currently

there are two ways 

(better easier, comfortable) create JDialog(JFrame parent, boolean true), with default close operation HIDE_ON_CLOSE, only one JDialog as local variable, reuse this Object by setVisible(false/true)
looping inside arrays of all JOptionPanes (all exists there untill current JVM is alive) by @kleopatra

