In Italy and most of Europe
the espresso and cappuccino cups are made of ceramic,
and bars go through so many so fast (hopefully for their business) that most of the cafes uses dish washers made specifically for cleaning cups.
On a commercial machine sold in Europe, there is an optional warmer switch heated either electrically or, less-usual, with steam. Basically, this is to bring the cups back to optimal temperature before being used again. However, the heat rising from a machine's boiler will still keep your ceramic cups hot, it will just take a little longer.
PS a little peculiarity
we common mortals always have the tendency to set cups on machine upside down
which to me makes sense, keep dust out etc etc
but a serious barista in Italy will put the cup facing up
the reason being:
the part of the cup that touches your lips shouldn't be the hottest one,
makes a really good point ......