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Код

private void jButton1ActionPerformed(java.awt.event.ActionEvent evt) {                                         
        try {
                jList1.setModel(model);
                int i = Integer.parseInt(jTextField1.getText());
                jTextField1.setText("");
                if (myThready.isAlive()) {
                    model.addElement(i);
                } else {
                    model.addElement(i);
                    myThready = new Thread(new Runnable() {
                        public int time = 10;
                        @Override
                        public void run() {
                            if (model.isEmpty()) {                        //есть ли у этого списка какие-либо компоненты (true - если нет)
                                return;
                            }
                            time = model.get(0);                                    
                            model.remove(0);
                            try {
                                Thread.sleep(time * 1000);
                            } catch (InterruptedException ex) {
                                Logger.getLogger(mainFrame.class.getName()).log(Level.SEVERE, null, ex);
                            }
                            System.out.println(time + "c\nПоток завершен!\n");
 
                            if (!model.isEmpty()) {
                                this.run();
                            }
                        }
                    });
                myThready.start();
            }
        } catch (NumberFormatException ex) {
            JOptionPane.showMessageDialog(rootPane, ex.getMessage());
            jTextField1.setText("");
        }
    }