Why doesn't my stainless steel Thermos get really really hot? Why doesn't my stainless steel Thermos get really really hot? Seems like a fairly straightforward question.

A few notes:

I was looking and found (obviously different values because steel is an alloy) that $$0.35~\mathrm{\frac{J}{g\,K}}\leq C_{p,\,\mathrm{steel}}\leq 0.55~\mathrm{\frac{J}{g\,K}}.$$
Obviously, that is just a rough range, but that is a very small heat capacity as is usual of metals.

Why then, does my 200 degree Fahrenheit coffee not heat up the stainless steel mug super quickly!

And even more baffling to me: Why in the world would it be a really good insulator?

It's entirely possible that I am devoid of any understanding of how insulation works, but I thought things which are bad conductors of electricity made good insulators. While stainless steel isn't praised for its electrical conductivity, I thought a material had to be about as bad as a gas at conducting electricity to be crowned with the title of "good insulator." I would just imagine that stainless steel, being metallic in many ways, would be a better conductor than that.

So what's going on? Why isn't my Thermos reaching 200 degree Fahrenheit?
I have a solid steel pint glass and I can tell you that it pretty much instantly heats up to the temperature of the liquid you put inside. You probably have some sort of double-wall vacuum flask, which insulates by using a vacuum between the steel.

As you can see, there are two walls to the flask: an inner wall and an outer wall. The inner wall is probably very close to the temperature of whatever is inside the flask. However, since the two walls are separated by a vacuum (which is a fairly good insulator), the outer wall, i.e. the one that you touch, remains pleasantly near ambient temperature*.
*Unpleasantly near ambient temperature, if you've been outside in a hot summer for a while.