I drink tea, and I like certain brands and kinds. I have tried asking the cafe attendant to put hot water directly into my own travel mug, but they won't do it (health department reasons I guess). They have always given me a cup of hot water free of charge. Then they turn and mark a piece of paper to account for the cup. I always leave a tip for the hot water. I hate having to take a paper cup when I have my own travel mug, which is much more pleasant to drink out of and doesn't instantly become another piece of trash. There have been occasions when dining car staff were willing to fill my travel mug directly.
I am going to try the thermos thing next time. The difference may be that health rules don't expect you to be drinking out of the thermos, so it's presumably not contaminated.