I’ve always put my thermos on the bottom shelf of my dishwasher. The cork and cup won’t hold up too well but then they can be hand washed.
I will second the “don’t clean it” sentiment. While it may not look nice, it will make the coffee taste better. Plus, if you get a good enough layer, anything you put in there will come out as coffee! Jonesin’ for a fix of caffeine? Just pour in some hot water, wait a little while, and like magic, coffee! I know people that have bragged about not having washed their coffee cups for years.
Oh yeah, and welcome to the SDMB, Murphy.
And Murphy, if Tzel offers you a cup of joe with that gracious welcome, it’s ok to politely decline. 
Peace,
mangeorge
Thank-you Tzel for the welcome and thank-you Mangeorge for the advice. Here’s wishing you both a happy new year and many cups of fresh brewed Columbian java.
Well, haven’t tried the alka seltzer because I just don’t have any on hand. I’ve heard the different suggestions that involve rice, ice, lemon juice, all those good things. I think they work only moderately well on the stainless steel. More of a glass coffee pot cleaner, if I remember correctly. I will try that CLR stuff and let you all know how it works.
As for drinking coffee out of the thermos, period - well, I work in an office where the coffee looks like water dressed in brown. It’s weak and out of a can. Instead, I grind up some beans, make myself some coffee, have one cup and take the remaining 2 cups to work with me in the thermos (it’s the perfect size!). It isn’t fresh from the pot but it isn’t so weak that I could fall asleep just looking at it. 
Tibs
Tiburon, why don’t you do what I do? I have a small coffee brewer at work, and a small grinder, and a small canister. I grind my coffee and brew my own 4-cup carafe of coffee, fresh, piping hot, and a nice aroma. Aaaaahh!
For 20 years I got brown stains in my coffee thermos…but NO MORE!
I started filtering my tap water through one of those pitchers with a filter cartridge in it and now the bottom of my thermos is perpetually bright and shiny. Not only that, but when I started using filtered water the stain that was already in the thermos disappeared. I’m serious.
If some chemist or food scientist can explain to me (1) what the brown stain is made of, and (2) why it doesn’t accumulate when I use filtered water, I would appreciate it.
I have absolutely no idea, Yeah, but I really like my
manual coffee grinder
It works great. Thanks, all.
Peace,
mangeorge