Is cup hotter than the drink itself

That sounds strange. I never had the same experience - if I use a ceramic cup, the cup never becomes hotter than the drink but it does become warm. If I use a glass and pour down the hot milk, then the whole glass is hot and I can't hold it, but the milk in it is still hotter. However, there is a valid explanation for your experience. If your cup absorbs the heat (law of conservation of energy says that it can be transferred - so the milk HAS to lose some of its heat when the cup grows hotter) but is made of material that hold the heat better than liquid then it can maintain that heat while the milk cools down (transferring the heat to air). :) That sounds about right. Thanks for the response on my discussion!

We do have cups at home that seemed to be hotter than the rest when placed in the microwave oven. These cheaper mugs were not exposed to certain heat when they were in the process of making it. Ceramics have their own classification that is why there are other ceramics called fine china. This types are made of porcelain and have been baked in the oven with right amount of heat over a period of time. They can be thick or thin but for sure they can withstand the heat of the food or liquid we place in it.

As in, the liquid is just hot, and there's nothing heating it up or anything, right? Well, I would have to say, the highest area of the container (assuming that there is a container) holding the liquid is the hottest. You've heard of convection, right? Where hotter liquids and gases rise up due to lighter density, and colder liquids and gases sink down due to heavier density. Same thing. Different parts of the liquid is assumingly at different temperatures, even if the difference is tiny. Any liquid that the slightly hotter than the rest will rise up to the surface. If it cools, then it will sink down, and any other liquid that is almost just as hot will rise up to take the sinking cold liquid's place. But of course, eventually, the liquid will cool to temperature of the surroundings...I hope that answered the question.