I think having the rear of the thing encased in the plastic box might make the heat issue worse by not allowing the hot air to exit the box. The rear panel is what serves as a heat sink, and should probably be exposed so that it can benefit from airflow.
Here's mine - a bit crude, but it works like a charm so far. Supplies required: glad wrap and velcro. Granted this is in a passat, but same deal - no mods to the car required.