It ought to be fine to add additional, LED, battery powered lights to the boot. The temperatures in there will be roughly similar to that in the cabin. Be sure the secure it sufficiently otherwise it may fall into your luggage.
As an alternative, you could replace the bulb in the existing light fitting in the boot with an SMD LED bulb. These are incredibly bright but produce little heat and draw little current, certainly less than the incandescent bulb that's in there. This gives you the advantage of not worrying about the battery in a self-contained light going flat.