The typical Japanese way to drink green tea is to brew it in a small (10 to 12 ounces) teapot and pour it into a small cup—roughly 4 ounces or so. The teapot keeps the tea hot, whereas the small tea cup allows just-poured tea to cool more quickly than a larger cup. (This is because a small cup has a higher ratio of surface ratio to volume.)
If you want your tea to stay hotter longer in the cup, then use a larger cup, such as an ordinary 8-ounce coffee mug. If you're using a small pot and large cup, so that the entire contents of the teapot fit into your cup, then this has the advantage of "stopping" the brewing process once you pour all the tea into the cup. Tea left sitting in a teapot too long will overbrew and end up quite bitter, so if you want to take your time drinking your pot of tea, you might want to pour it all into a big cup that will stop the brewing process and keep your green tea hot longer than a small cup would.