The BPPC is a little oven, especially inside a desktop case.
You'll have to raise the A1200 on higher legs, to clear more space for airflow.
I have an A1200 with BPPC+BVision inside.
It has 2 fans attached to the top grill, it is raised by 1.5cm and there's a fan glued to the trapdoor, which is drilled full of holes for airflow.
Even with all that, during summer days the bottom gets quite hot to the touch.