Often, (unless the hotel is at 100% capacity), arriving guests are given a room that was not occupied the previous night. It's highly unusual that anyone would cook food inside the carafe. Even if they did, if it hasn't been used in 24 hours, any leftover taste is considered to damage food/drink, and is thus permitted.
Yoreh Deah 122 teaches the rule of "eino ben yomo" (not used in 24 hours). It rules there that a vessel which certainly cooked nonkosher food in the past, should still not be used. This stricture is a rabbinic enactment, lest someone use a pot he thought was "eino ben yomo", but it turns out it was actually "ben yomo". (used within the last 24 hours).
In our case, we are dealing with a vessel that probably didn't cook anything but coffee. Therefore, the rabbinic stricture of not using an "eino ben yomo" doesn't apply, since it only applies to vessels which certainly cooked nonkosher food.
The Chicago Rabbinical Council (CRC) also rules along these lines.