In the context of car braking transferring energy to the thermal energy store of the brakes and surroundings, what force causes this energy transfer?

What the question is really asking

You are being asked to name the force that does work to slow the car down. The force doing the work is the one responsible for turning the car’s kinetic energy into heat.

Where the energy goes during braking

When the brakes are applied, the car’s kinetic energy decreases. That energy is transferred mainly into the thermal energy store of:

• the brake pads and discs (or drums), and
• the nearby air and surrounding parts.

The force that makes the transfer happen

The key force is friction:

• Friction between brake pads and the disc/drum produces heating in the brakes.
• Friction between tyres and the road also contributes, especially at the contact patch.

Because friction acts opposite the motion, it does work on the moving car. In simple terms, the work done by friction is $$W = Fd,$$ and this work appears as increased thermal energy.