Not all places on the equator are very warm. This is because elevation plays a key role in climate, so mountain ranges on the equator can still be cold at a certain height.
Two examples of areas that are close to the equator but remain cold due to elevation are the Andes mountains and Mount Kilimanjaro in Tanzania, which even has glaciers. This results in animals that seem unlikely for regions that lie within the tropics, such as alpacas and llamas. However, the equator does receive more direct sunlight than the rest of the world, so when elevation is around sea level, it is always tropical.