Why does tea in an ordinary aluminium kettle cool down fast?

It's all about the size of an object, heat is a form of energy and the larger an object the more energy it can store, a teapot is considerably larger then a teacup, so the teapot holds more heat energy and therefore cools down slower then the teacup which holds less energy as it is smaller

Or it could be because the boiling water in a teapot is completely surrounded by material so it has no where to lose it's heat except through the spout, a teacup has no lid so the heat can escape into the air around it