How do I plan an essay under such strong time constraints?

Ultimately, in exam conditions you have to prioritise speed during the planning time, as usually you only have about 45 minutes to write each essay. Therefore, plans have to be simple and different buzzwords and thematic heading are the easiest way to organise your thoughts and get the best out of the ideas in your head. For me, I always started with a spider diagram, with the theme of the essay at the centre, and then each paragraph had its own 'leg' with quotes and main ideas. This visual representation of your plan allows you to make sure you don't miss out any important ideas, and is easy to refer to during the writing time if you get lost. Simplicity is key!