Ritergal, I really like your idea of throwing it into the fireplace. It reminds me of a technique that my own therapist taught me years ago, which was to, as I was writing, visualize the thoughts going from my head, down my arm, through my hand, and out the pen onto the paper. Then I would leave the thoughts on the paper and be able to walk away from them until I needed to pick them up again, at which time they would be safely waiting on the paper for me to pick them up again. It was a helpful exercise because I was often exhausted from lack of sleep due to nightmares about my childhood during that time in my life. After my therapist taught me this technique, when I awoke with a nightmare, I would write it down, leave it on the paper, and then be able to get some good sleep.
I later developed a similar exercise for my own clients where they would visualize a cloth bag (I would ask them to tell me what it looked like - size, color, etc - to help enhance the visualization) next to the door inside my office. When they left at the end of a session, they visualized placing their painful thoughts and feelings in the bag, where they would be waiting for them to take them out again at the start of the next session. This exercise enabled them to leave that unhappiness in the therapy office so that they could function more productively at home between sessions. It can be so hard for adults to be good parents, students to be good students, etc, when they are in the throes of their own pain.
It sounds like your class may actually be providing some therapeutic benefits to your students, but if it starts to cause problems for them, as Sakamonda suggests, it might be a good idea to refer them for counseling. How wonderful that they have a sensitive teacher in you.