Practically all coffee mugs and teacups are badly designed. In two ways.
First, the opening is too wide, so the coffee or tea cools down quickly. Mugs should be shaped like an inverted funnel, with a narrow opening . Not as narrow as a funnel — it should be wide enough for you to reach inside to clean. But as narrow as possible subject to this constraint.
Worst of all are mugs that widen to the top. The tea cools down too quickly, so you have to gulp it down before it does, rather than savouring your drink. One step better are mugs or cups with straight sides, because the opening is at least no wider than the bottom. But best of all would be a tapered mug with a narrow opening.
Second, mugs should have a built-in straw that goes to the bottom. That lets you drink the coldest part of the tea first. A problem with existing mugs is that by the time you get to the bottom, you're left with lukewarm tea that you then have to throw away. Physics tells us that hot tea rises to the top, and cold tea sinks to the bottom. Drink the cold tea first, before it gets any colder and has to be thrown away.
If you stop and think for a second, mugs that make you throw away part of the drink have failed at their job. Imagine if your car were designed so that every time you refuel, the bottom 10% of fuel in the tank must be thrown away. We'd consider that unacceptable. Coffee mugs perform no better. Why are they somehow considered acceptable?
Drinking the cold part first also helps near the beginning, when the hot tea is too hot to drink. For both reasons, drink the cold part first, saving the hot part for the end, not the other way around, as with mugs today.
A straw also lets you blow bubbles in, which is a better way of cooling the tea than blowing from the top. That's because, when you introduce air at the bottom, it takes some time to rise, so it's in contact with the tea for longer, absorbing more heat. It's also in contact with the tea on all sides, rather than just the bottom (when you blow air at the top surface). Both these factors cool the tea faster.
It's surprising that most designers of mugs haven't realised such basic scientific and in fact common-sense facts, and instead blindly imitate one another as they continue designing second-rate mugs. Isn't it strange that a civilisation advanced enough to send a probe out of its solar system hasn't yet figured out how to make sensible teacups?