I want to tell you why I leave the top off when I order hot coffee. Half the time, I don't even take a plastic top with me out of the shop, and that's because I like my coffee to get cooled off, even all the way down to a lukewarm, room-temperature level.
Weird, right? Let me defend and explain. Coffee is brewed at temperatures ranging between 195°F and 205°F. You pretty much have to brew between these temps -- anything hotter produces a burnt taste, and anything cooler won't extract enough coffee flavor particles out of the grounds.
If you're handed a fresh-brewed cup, or something out of an insulated dispenser, your coffee is probably between 170°F and 180°F (McDonald's coffee is on the higher end of that, for reference). In a regular paper to-go cup, coffee loses its heat pretty quickly, and many people are comfortable with drinking it around 150°F. At that point, and down to approx. 130°F, the heat stops overpowering the taste, and the real flavors of the coffee come through.
Now, below 120°F is when most people start looking for a microwave, or worse, THEY THROW THE COFFEE AWAY. Which leaves me aghast because, for me, this is when coffee really becomes its best. When coffee cools off, the flavors become sweet and acidic, like lemonade. The colder a coffee gets, the more of the delicate, floral notes come forward to play. This is why in professional coffee cuppings, tasters will often return to cups once they've cooled down, in order to note the subtler flavors. This is also why iced coffee is so damn delicious, especially when brewed with a single-origin.
So, how hot do you like your coffee? Are you willing to try it at a different temperature? If you order a single-origin pourover, or want to simply experience two vastly different cups of regular drip coffee, sip half of your next cup while it's hot, then wait a while and finish it when it's cool. If you like what you taste, maybe you'll start leaving the top off, too.