Fire under rear seat 1988 735i

On the way to work the other day all the lights starting flashing on and off, with numerous messages appearing on the on-board computer. One was trunk open. I was sure the trunk was closed, but I checked any way. Upon opening the trunk, I found it full of smoke! The rear tailight was out, so I assumed it was a short. I drove on to work. All interior light remained on, windows and sunroof did not work, central locking also did not work. When I got to work, I couldn't get the interior lights to go out so I pulled the rear seat to disconnect the battery. The entire bottom of the rear seat was charred, and the computer opposite the battery was completely burnt and melted. The wires going to this unit seem to be in pretty good shape.

Does anyone know what caused this? What is the name of that compute and is it worth trying to change it?

The car only has 150,000 miles and runs fantastic. Thanks for any help.