I have learnt coffee oxidizes quite fast giving that horrible burnt taste, which even milk won’t hide. The longer it has been in a open-to-air-pot, the worse the taste gets. Storing in an air-tight container (thermos) it stays “ok” for days. So actually, I think all such servings from the coffee shops are thus inherently worse than brewing your own coffee.
(There are no starbucks in my country, but I think McDonald’s coffee really is somehow heated past 100*C and it’s the first sip away to burn your mouth, so you wouldn’t taste it anyway.)