In Heat: Pedal to the Metal, when taking a corner while over the speed limit, where do the spent Heat cards move from the engine?

In the popular racing board game "Heat: Pedal to the Metal": when my car passes through a corner with a speed limit of 2, its total speed reaches 5 (3 over the limit). I must spend 3 Heat. Question: are these 3 Heat cards taken from the Engine area into my hand, or discarded directly into the discard pile?