Thermos ... it keeps hot things hot, and cold things cold.  How does it know?  :-)

There are also a few bike accessory companies that make modified water bottle cages to fit thermos bottles, as well as one or two that make handlebar mounted cages for cups/travel mugs.  I can't personally vouch for either (I put my thermos in my pannier) but I know these products are available.

I used to have a handlebar mount drink holder on my bike.  It worked very well although large bumps could cause the cup to get a little lose and you definitely need a lid.  I did not use it for coffee but it is designed to hold your typical to-go coffee cup.  I used it for less legal beverages on midnight rides for which it worked extremely well.  I moved and sold that bike and have not added it to my new bike but certainly would.  This is not designed for a Thermos however.

I just saw Sigg makes an insulated bottle but I have not tried it.  Sigg makes aluminum bottles out of recycled material with water based liners inside.  They are a little pricey but very lightweight, sturdy, and healthier than drinking bisphenol-A out of plastic bottles.  I recommend an un-painted bottle or using a plastic cage since the metal cages tend to scratch the paint.

The transport of hot caffeinated beverage has been essiential to my commute for years.  My coffee would stay hot enough in a little thermos even after a 25 minute ride at 25F.  Now that I shop by bike as well, I have neoprene sleeves designed for taking wine on a picnic (Every week is a picnic for us!).  Combining the two would preserve heat and lessen the risk of breakage.  My current commute is much shorter and I have taken to drinking all my coffee at home, but my coffee cup fits in my water bottle holder, so I can cart a beverage around town.

I just wanted to comment that I was very happy that Umbra used this as an opportunity to infuse a little bit of physics in her answer (i.e. heat xfer mechanisms and how they were).  Nice job! :)

Funny - when I saw the headline for this Umbra column, I thought it referred to Project Rwanda and the "real" coffee bikes! If you are not familiar, check out projectrwanda.org, in particular, the Coffee Bike tab. You can support this great project, or even get your very own coffee bike, limited edition and signed by Tom Ritchey! :)

I have two nearly antique Stanley Co. vacuum flasks. These work very well in maintaining the temperature of whichever liquid you may be carrying. I definately would stay away from the glass-lined models as they are almost worthless when you take them out and about. Recalling my elementary school years, I have good memories of breaking not one, but two, glass-lined flasks. Break a glass-lined flask, and it's off to the landfill. Steel-lined is the way to go: no leaching of any nasty synthetic chemical and the damn things are practically bullet-proof. I found one my flasks at a resale/antique shop, and the other one is practically a family heirloom. That's abother good thing about used: no new resources were used to manufacture it. 'Tho' I will concede that the steel in any new product is almost certainly rrecycled. Metals recycling is one of the biggest businesses out there. Getting the natural cork stoppers, though, is getting harder to do. Oh, one of the other peculiarities of a vacuum flask with a natural cork stopper is that the darn things can be a BEAR to open. Seems the cork gets drawn, basically, further into the spout during the time you fill it and the first time you actually use it. Watch that coffee, it will be HOT!

I agree, steel is definitely the way to go.  I've dropped mine countless times without breaking it.  One think I would suggest for soymilk drinkers out there is to store it separately from the coffee if it's going to be a while before drinking it.  In my experience, the heat changes the flavor of the soymilk (denatured proteins and whatnot) over time to something quite nasty.  

Also, if you're spending a lot of time in the heat/sun the giant quart-sized Thermoses keep water nice and chilly all day in the direct sun!