than the lightbulb inside your fridge, and will cost next to nothing to run. It's designed to be left on for very long periods, and as long as there is nothing (like a book or magazine) placed on top it will be fine. It needs air circulation to keep cool.
Having said that, I never leave my router on all night - it's unnecessary and means that you are sitting there on a fixed IP address, which is never a good thing for a home computer. Turn it on in the morning and off again when you go to bed.