Wheel dust shields won't make a measurable difference in rotor cooling- more cooling is done by conduction through the wheels, axle, pad and caliper than by air on the rotor. Those are cooled by the surrounding air, and suffer no paucity of flow from having dust covers installed. The centrifugal flow of air pumped by the wheels -regardless of design- will more than overcome any "shrouding" the dust covers (which are vented) might provide. They'll help keep water off them in the rain, as well.
Sounds like the part your bent was the rear dust shield.
On drum brakes, it's called the brake backing plate, and it's what the shoes, and from there the rest of the car, are attached to. They're what transfer braking torque to the chassis.
On disc brakes, the dust shield keeps mud and crap off the rotor. The wheel is supposed to keep the outside clear.