Insulation for apartment with none in the ceiling.

Our apartment ceiling is wood without insulation and our AC is weak wall units. In hot SoCal this doesn't work. We're looking for a cheap, temporary fix for the next few years we rent here.

Here's the very silly question: is it a good option to buy rolls of insulation and wedge them between the beams, running a wire the length of the room to hold it up?

Living room pictured below, though entire apartment needs this fix:

Beam depth: 5.25"

Each section between beams: 25.5"x136"